We provide the triangle and its properties practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on the triangle and its properties skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of the triangle and its properties Questions

Question No | Questions | Class |
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1 | A tower of height b and a flagstaff on top of tower subtend equal at a point on the ground, distant a from the base of the tower. The height of the flagstaff is A ( cdot frac{b^{2}}{a+b} ) B. ( frac{b(a+b)}{a-b} ) c. ( frac{b^{2}}{a-b} ) D. ( bleft(frac{a^{2}+b^{2}}{a^{2}-b^{2}}right) ) |
7 |

2 | Find ( ^{prime} x^{prime} ) for the given figure below | 7 |

3 | 11. Let PQRS be a rhombus, find x, y. 10. 11. |
7 |

4 | In ( Delta ) ABC ( angle A=65^{0} ) and ( angle B=25^{circ} C ) Name the hypotenuse. |
7 |

5 | ( angle B C A ) | 7 |

6 | Construct a ( triangle A B C ) in which the base ( B C=5 mathrm{cm}, angle B A C=40^{circ} ) and the median from ( boldsymbol{A} ) to ( boldsymbol{B} boldsymbol{C} ) is ( boldsymbol{6} mathrm{cm} . ) Also measure the length of the altitude from ( A ) |
7 |

7 | Find the value of the unknown exterior ( x ) in the following diagrams. |
7 |

8 | In the adjoining figure ( A B= ) ( 12 mathrm{cm}, C D=8 mathrm{cm}, angle A B D= ) ( angle A E C angle E D C=90^{circ} . ) If ( B E=x, ) then A. ( x ) has two possible values whose difference is 4 B. ( x ) has two possible values whose sum is 2 c. ( x ) has only one value and ( x geq 12 ) D. ( x ) cannot be determined with the given information |
7 |

9 | AD bisects angle ( A ) of triangle ( A B C ) where D lies on BC and angle ( mathrm{C} ) is greater than angle B. then angle ADB is greater than angle ADC. A . True B. False |
7 |

10 | Which of the following sets of side lengths will not form a triangle? A. ( 11 mathrm{cm}, 10 mathrm{cm}, 11 mathrm{cm} ) в. ( 3 mathrm{m}, 3 mathrm{m}, 3 mathrm{m} ) ( mathbf{c} .9 mathrm{mm}, 9 mathrm{mm}, 12 mathrm{mm} ) D. ( 3 mathrm{cm}, 4 mathrm{cm}, 7 mathrm{cm} ) |
7 |

11 | In an isosceles ( triangle A B C ) is the ( A B=A C ) ( D ) and ( E ) are points on ( B C ) such that ( B E=C O ) show that ( A D=A E ) |
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12 | ( A B C ) is a right angled triangle is which ( angle A=90^{circ} ) and ( A B=A C . ) Find ( angle B ) and ( angle C ) |
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13 | If in two triangles ( A B C ) and ( P Q R ) ( frac{A B}{Q R}=frac{B C}{P R}=frac{C A}{P Q} . ) Write a relation between the two triangles. |
7 |

14 | In the given Fig f ( boldsymbol{A B} | boldsymbol{C D}, boldsymbol{E F} perp boldsymbol{C D} boldsymbol{a n d} angle boldsymbol{G} boldsymbol{E D}= ) ( 126^{circ}, ) Find ( angle A G E, angle G E F, angle F G E ) |
7 |

15 | In a ( triangle A B C, ) perpendicular ( A D ) from ( A ) on ( B C ) meets ( B C ) at ( D . ) If ( B D=8 mathrm{cm} ) ( D C=2 mathrm{cm} ) and ( A D=4 mathrm{cm}, ) then A. ( triangle A B C ) is isosceles B. ( triangle A B C ) is equilateral c. ( A C=2 A B ) D. ( triangle A B C ) is right angled at ( A ) |
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16 | Find the measure of each angle of an equilateral triangle. |
7 |

17 | Find ( y ) ( mathbf{A} cdot 45^{circ} ) B ( .60^{circ} ) ( c cdot 15^{c} ) D . 20 |
7 |

18 | In an isosceles triangle ( A B C ) with ( A B= ) ( A C, B D ) is perpendicular from ( B ) to the side AC. Prove that ( B D^{2}-C D^{2}= ) ( 2 C D . A D ) |
7 |

19 | ( ln a Delta A B C, I f A C>A B ) and the bisector of ( angle A ) meets ( B C ) at ( E ), then A. ( C E>B E ) в. ( C E B E )D. ( C D<B E ) |
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20 | In the given figure, ( boldsymbol{O} ) is a point in the interior of ( 1 M ) a square ( A B C D ) such that ( O A B ) is an equilateral triangle. Show that ( O C D ) is an isosceles triangle. |
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21 | ( angle boldsymbol{A}+angle boldsymbol{B}=mathbf{6 5}^{circ}, angle boldsymbol{B}+angle boldsymbol{C}=mathbf{1 4 0}^{circ} ) Find measure of each angle of ( Delta ) |
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22 | If two angles in a triangle are ( 65^{circ} ) and ( 85^{circ}, ) then the third angle is: ( A cdot 30 ) B . 45 ( c cdot 60^{circ} ) D. ( 90^{circ} ) |
7 |

23 | In the figure given, lines ( X Y ) and ( M N ) intersect at ( 0 . ) If ( angle P O Y=90^{circ} ) and ( a: b= ) ( 2: 3, ) then ( angle X O N ) is equal to A . ( 126^{circ} ) B . ( 30^{circ} ) ( c cdot 90^{circ} ) D. ( 180^{circ} ) |
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24 | Find the name of the triangle. A. isosceles B. equilateral ( c . ) scalene D. acute |
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25 | ( ln Delta mathrm{ABC}, overline{X Y} ) is paralled to ( overline{A C} ) and divides the triangle into two parts of equal area. Then the ( frac{A X}{A B} ) equals A ( cdot frac{sqrt{2}+1}{2} ) B. ( frac{2-sqrt{2}}{2} ) c. ( frac{2+sqrt{2}}{2} ) D. ( frac{sqrt{2}-1}{2} ) |
7 |

26 | An obtuse triangle will have one and only one angle. A . acute B. obtuse c. scalene D. right angled |
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27 | Find the values of ( x ) and ( y ) in the given triangles, where ( angle A=70^{circ}, angle B= ) ( mathbf{3 6}^{circ}, angle boldsymbol{D}=mathbf{6 8}^{circ} ) and ( angle boldsymbol{F}=mathbf{5 6}^{circ} ) A ( . x=103, y=80 ) B . ( x=105, y=75 ) C ( . x=105, y=87 ) |
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28 | If in a triangle ( boldsymbol{L} boldsymbol{M} boldsymbol{N} ) ( angle M=60^{circ}, angle N=60^{circ}, ) find ( angle L ) Mention the kind of triangle also. |
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29 | In triangle ( A B C, 3 angle A=4 angle B=6 angle C . ) The smallest angle of the triangle is ( 50^{circ} ) A. True B. False |
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30 | A triangle can have: A. Two right angles B. Two obtuse angles C. All angles more than ( 60^{circ} ) D. Two acute angles |
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31 | ( triangle A B C ) is right angled in which ( angle A= ) ( 90^{circ} ) and ( A B=A C . ) Find ( angle B ) and ( angle C ) |
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32 | In a triangle, there are 3 different angles.Which of the following statements is/are definitely true about the angles? (i) Sum of all the angles is ( 100^{circ} ) (ii) One angle is obtuse and other two are acute and right angle respectively. (iii) Sum of any two angles is always less than ( 180^{circ} ) A. (ii) only B. (ii)and (iii) both c. (iii) only D. (i) and (iii) both |
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33 | It is not possible to construct a triangle with which of the following sides? A. ( 8.3 mathrm{cm}, 3.4 mathrm{cm}, 6.1 mathrm{cm} ) B. ( 5.4 mathrm{cm}, 2.3 mathrm{cm}, 3.1 mathrm{cm} ) c. ( 6 mathrm{cm}, 7 mathrm{cm}, 10 mathrm{cm} ) D. ( 3 mathrm{cm}, 5 mathrm{cm}, 5 mathrm{cm} ) |
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34 | Angles opposite to the equal sides of a triangle are equal.ff true enter 1 else 0 | 7 |

35 | Find the measures of the third angle in degrees ( 92^{circ}, 27^{circ},—- ) |
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36 | A piece of wire ( 28 mathrm{m} ) long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How much wire should be used for the square in order to maximize the total area? |
7 |

37 | Fill in the blank All ( dots dots dots dots dots ) triangles are similar A. equilateral B. scalene c. isoceles D. None of these |
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38 | Verify the points (0,7,-10)(1,6,-6) and (4,9,-6) are the vertices of an isosceles triangle. | 7 |

39 | The sum of lengths of any two sides of a triangle is always the third side. A. greater than B. less than c. equal to D. none of these |
7 |

40 | Consider the points ( boldsymbol{P}(mathbf{2},-mathbf{4}) ; boldsymbol{Q}(mathbf{4},-mathbf{2}) boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{R}(mathbf{7}, mathbf{1}) . ) The points P,Q,R A. form an equilateral triangle B. form a right angled triangle c. form an isosceles triangle which is not equilateral D. are collinear |
7 |

41 | n Fig., the side ( Q R ) of ( triangle P Q R ) is produced to a point ( S ) If the bisectors of ( angle P Q R ) and ( angle P R S ) meet at point ( T, ) then prove that ( angle mathrm{QTR}=frac{1}{2} angle mathrm{QPR} ) |
7 |

42 | ( ln triangle A B C, A B=B C=K, A C=sqrt{2} k, ) then ( triangle A B C ) is a : This question has multiple correct options A. Isosceles triangle B. Right-angled triangle c. Equilateral triangle D. Right isosceles triangle |
7 |

43 | If three altitudes of a triangle are equal then the triangle is A . Right angled B. Equilateral c. Isosceles D. Scalene |
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44 | ( triangle A B C ) is iscoeles in which ( A B=A C ) ( operatorname{seg} B D ) and ( operatorname{seg} C E ) are medians show ( operatorname{that} B D=C E ) |
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45 | In the adjoining figure, find the measure of ( angle B C D ) |
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46 | ( ln Delta A B C, A D ) is drawn such that ( Delta A B D ) and ( Delta A C D ) are equal in area then, the AD is A. any segment drawn from A to BC B. the bisector of ( angle B A G ) c. A median of ( Delta A B C ) D. None of these |
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47 | Find the values of ( x ) and ( y ) in the following figures A ( . x=80^{0} ; y=120 ) В . ( x=50^{0} ; y=30^{0} ) C . ( x=50^{circ} ; y=130^{circ} ) D . ( x=20^{0} ; y=10^{0} ) |
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48 | ( A ) and ( B ) are two fixed points in a plane. If Pis a moving point in the plane such that ( P A=P B, ) then the: A. locus of P is the line AB itself. B. locus of P is a line parallel to AB c. point P always makes equilateral triangles with A, B. D. triangle PAB is isosceles for all positions of P. |
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49 | The point 0 lies inside a triangle ( P Q R ) such that ( Delta O P Q, Delta O Q R ) and ( Delta O R P ) are equal in area. Then,the point 0 is called as A. incentre B. centroid c. circumcentre D. orthnocentric |
7 |

50 | ( boldsymbol{P Q}=boldsymbol{Q} boldsymbol{R}=boldsymbol{P S} . ) Calculate the size of the labelled angles. B . (b) ( a=42^{circ}, b=48^{circ}, c=69^{circ}, d=111^{circ} ) C . (c) ( a=45^{circ}, b=45^{circ}, c=67.5^{circ}, d=112.5^{circ} ) D cdot (d) ( a=50^{circ}, b=40^{circ}, c=65^{circ}, d=115^{circ} ) |
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51 | ldentify the largest side of the triangle. f the angles are given as: ( angle A=50^{circ}, angle B=10^{circ} ) and ( angle C=22^{circ} ) ( A cdot overline{A B} ) 8. ( overline{B C} ) ( c cdot overline{C A} ) ( D . overline{A C} ) |
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52 | ( ln Delta A B C, 2 angle A=3 angle B=6 angle C . ) Find ( frac{angle A+angle B}{angle C} times angle B ) |
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53 | In the figure, ( angle P Q R=angle P R Q, ) then prove that ( angle P Q S=angle P R T ) |
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54 | In the figure given below, the value of ( (angle x+angle y) ) is : 4. ( 110^{circ} ) B . ( 100^{circ} ) ( c cdot 120 ) D. ( 60^{circ} ) |
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55 | The sides of a triangle with positive area have lengths 5,7 and ( a . ) The sides of a second triangle with positive area have lengths 5,7 and ( b ) Which of the following is NOT a possible value of ( |boldsymbol{a}-boldsymbol{b}| ? ) A . 3 B. 5 ( c cdot 7 ) D. 10 |
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56 | Angles opposite to equal sides of an isosceles triangle are equal. Prove this result |
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57 | Assertion: An isosceles ( Delta ) is right angled. Reason ( : angle A=angle B=45^{circ} ) and ( angle C= ) ( mathbf{9 0}^{circ} ) Which of the following statement is true? A. A is true and ( mathrm{R} ) is the correct explanation of B. A is true and R is not the correct explanation of c. A is false D. None of these |
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58 | In a triangle, the Sum of two angles is 118 and their difference is ( 32 . ) find each angle of the triangle. A. 75,43 and 62 B. 85,33 and 62 c. 65,53 and 62 D. none of the above |
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59 | In the triangle, find the measures of the angles. A ( cdot 40^{circ}, 60^{circ}, 80^{circ} ) B ( cdot 45^{circ}, 60^{circ}, 75^{circ} ) c. ( 45^{circ}, 45^{circ}, 90^{circ} ) D. ( 50^{circ}, 60^{circ}, 70^{circ} ) |
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60 | In the figure at right, ( A B ) and ( C D ) are straight lines through the centre 0 of a circle. If ( angle A O C=98^{circ} ) and ( angle C D E= ) ( mathbf{3 5}^{circ} ) Find (i) ( angle D C E ) (ii) ( angle A B C ) |
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61 | If ( left(x_{1}, y_{1}, z_{1}right) ) and ( left(x_{2}, y_{2}, z_{2}right) ) are two vertices and ( (alpha, beta gamma) ) is the centroid of a triangle, find the third vertex of the triangle. | 7 |

62 | If ( Delta A B C ) is an equilateral triangle of side ( a ) and ( mathrm{D} ) is a point on ( B C ) such that ( B D=frac{1}{3} B C ) then the prove that ( A D= ) ( frac{sqrt{7} a}{3} ) |
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63 | Using triangle inequality theorem check whether the given side lengths ( boldsymbol{a}=mathbf{3}, boldsymbol{b}=mathbf{5} ) and ( boldsymbol{c}=mathbf{1} ) will form a triangle or not |
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64 | n Fig. ( angle boldsymbol{P}=mathbf{5} mathbf{2}^{circ} boldsymbol{a} boldsymbol{n} boldsymbol{d} angle boldsymbol{P} boldsymbol{Q} boldsymbol{R}=boldsymbol{6} boldsymbol{4}^{circ}, ) i ( Q O ) and ( R O ) are the angle bisectors of ( angle P Q R ) and ( angle P R Q ) respectively, then find the values of ( angle x ) and ( angle y ) |
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65 | Find the values of ( x ) and ( y ) in the figure given below |
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66 | If the two angles of a triangle are unequal, then the smaller angle has the side opposite to it. A. Smaller B. Larger C. May be smaller may be larger D. The side will be equal to one of the opposite sides |
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67 | If each side of an equilateral triangle is 8, calculate the length of the altitude. A . 1.73 B . 2 c. 3.46 D. 4 E . 6.93 |
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68 | The centroid of the triangle whose vertices are (4,-8),(-9,7) and (8,13) is в. (1,3) c. (1,5) (年. (1,5) D. (1,9) |
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69 | In the given figure shown ( boldsymbol{P Q R S} ) is a square and ( S R T ) is an equilateral triangle then state whether ( angle Q T R= ) ( 15^{circ} ) is true/false. A. True B. False |
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70 | ( Delta A B C ) is an isosceles right triangle with area ( P . ) The radius of the circle that passes through the point ( A, B ) and ( C ) is: ( A cdot sqrt{P} ) B. ( sqrt{frac{P}{2}} ) c. ( frac{sqrt{P}}{2} ) D. ( sqrt{2 P} ) |
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71 | In the following figure, ( S ) is any point on side ( mathrm{BC} ) of ( Delta mathrm{ABC} Delta mathrm{ABC} ). Then ( mathrm{AB}+mathrm{BC}+mathrm{CA} ) २२४S A. True B. False |
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72 | ( Delta A B C ) is an isosceles triangle with ( A B=A C . A D ) bisects ( angle A . ) Prove that ( angle B=angle C ) |
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73 | The perimeters of an equilateral triangle and a square are same The area of triangle : area of square is A . 1: 1 в. ( 4: 3 sqrt{3} ) c. 4: 3 D. 3: 2 |
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74 | In a triangle ( A B C, angle A+angle B=144^{circ} ) and ( angle A ) ( +angle C=124^{circ} ) Calculate each angle of the triangle. A ( cdot A=88^{circ}, B=56^{circ} ) and ( C=36 ) B. A ( =78^{circ}, B=66^{circ} ) and ( C=36^{circ} ) C. ( A=58^{circ}, B=86^{circ} ) and ( C=36^{circ} ) D. ( A=88^{circ}, B=26^{circ} ) and ( C=66^{circ} ) |
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75 | Identify the largest angle of the triangle. ( A ) в. ( c ) ( D ) |
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76 | The number of lines of symmetry in a scalene triangle is A. 0 B. ( c cdot 2 ) ( D ) |
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77 | n the given figure, ( triangle A B C ) is an equilateral triangle and ( square A W X B ) and ( square A Y Z C ) are two squares. The value of ( frac{1}{10}(angle Z X A) ) is: |
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78 | In the adjoining figure find the values of ( x ) and ( y ) |
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79 | The combined equation of the three sides of a triangle is ( left(x^{2}-y^{2}right)(2 x+3 y-6) . ) If the point ( (0, a) ) lies in the interior of this triangle then A ( .-2<alpha<0 ) B. ( -2<alpha<2 ) c. ( 0<alpha<2 ) D. ( alpha geq 2 ) |
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80 | An equilateral triangle has lines of symmetry. A. 0 B. ( c cdot 3 ) ( D ) |
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81 | In the given figure, find ( angle boldsymbol{P} boldsymbol{N} boldsymbol{M} ) |
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82 | Construct ( triangle A B C ) with ( A B= ) ( 5 c m, B C=5 c m ) and ( A C=5 c m ) |
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83 | n ( triangle boldsymbol{P Q R}, boldsymbol{P Q}=boldsymbol{P R}, angle boldsymbol{Q}=mathbf{6 5}^{circ} ) then find ( angle P ) |
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84 | ( A D, B E ) and ( C F, ) the altitude of ( Delta A B C ) are equal. Then ( mathbf{A} cdot A C=B C ) B . ( A D=A B ) c. ( A B=C F ) D. None of these |
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85 | Identify the triangle as equiangular, acute, obtuse or right. Answer: Obtuse Mark answer as 1 if true else 0 if false |
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86 | n given figure the interior opposite angles of the exterior angle ( angle A C D ) are: ( A cdot angle B, angle C ) в. ( angle A, angle C ) ( mathbf{c} cdot angle A, angle B ) D. ( angle B, angle E ) |
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87 | ( P ) is any point inside the triangle ( A B C ) Prove that: ( angle B P C>angle B A C ) | 7 |

88 | A triangle has side lengths of 6 inches and 9 inches. If the third side is an integer, calculate the minimum possible perimeter of the triangle (in inches). A . 4 B. 15 c. 8 D. 19 E . 29 |
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89 | The sides of a triangle are ( mathbf{5 0} mathrm{cm}, mathbf{7 8} mathrm{cm} ) and ( 112 mathrm{cm} . ) The smallest altitude is… ( mathbf{A} cdot 20 mathrm{cm} ) B. ( 30 mathrm{cm} ) c. ( 40 mathrm{cm} ) D. ( 50 mathrm{cm} ) E. None of these |
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90 | Name the type of following triangle. ( Delta X Y Z ) with ( m angle Y=90^{circ} ) and ( X Y=Y Z ) |
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91 | In an isosceles triangle, the base angles are equal. The vertex angle is ( 40^{circ} . ) What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is ( 180^{circ} ) ). |
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92 | Compute the value of ( x ) in the figure given |
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93 | ( mathbf{n} Delta boldsymbol{P} boldsymbol{Q} boldsymbol{R}, angle boldsymbol{P}=mathbf{2} boldsymbol{x}+mathbf{1}^{circ}, angle boldsymbol{Q}=mathbf{3} boldsymbol{x}+ ) ( mathbf{3}^{circ} boldsymbol{a} boldsymbol{n} boldsymbol{d} angle boldsymbol{R}=boldsymbol{x}+boldsymbol{2}^{circ} . ) What is the value of x? |
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94 | Calculate ( angle B A C ) ( A cdot 90^{circ} ) B ( .50^{circ} ) ( c cdot 60^{circ} ) ( mathbf{D} cdot 80 ) |
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95 | Find the value of the unknown interior angle ( x ) in the following figure. |
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96 | The angles in a Quadrilateral are ( x, 5 x, 2 x+10, x+80 ) Find ( x ) A . 30 B . 18 ( c .35 ) D. 42 |
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97 | Prove that the lines represented by ( 3 x^{2}-8 x y-3 y^{2}=0 ) and ( x+2 y=3 ) From the sides of an isosceles right angled triangle. |
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98 | In the figure above, points ( A, D, B, ) and ( G ) are collinear. If ( angle C A D ) measures ( 76^{circ} ) ( angle B C D ) measures ( 47^{circ}, ) and ( angle C B G ) measures ( 140^{circ}, ) find the degree measure of ( angle boldsymbol{A} boldsymbol{C} boldsymbol{D} ) A ( cdot 12^{circ} ) B . ( 14^{circ} ) ( c cdot 17 ) ( mathbf{D} cdot 36 ) ( E cdot 43 ) |
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99 | In the adjacent figure value of ( x ) ( mathbf{A} cdot 67^{circ} ) В. 157 ( mathrm{c} cdot 179^{circ} ) ( mathbf{D} cdot 360^{circ} ) |
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100 | What is the largest side of the triangle? A. ( overline{A B} ) в. ( overline{B C} ) ( c cdot overline{C A} ) D. ( overline{A C} ) |
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101 | Two triangles having the same base (or equal bases) and equal areas lie between the same parallels |
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102 | In the adjacent triangle ( A B C ), find the value of ( x ) and calculate the measure of all the angles of the triangle. |
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103 | Find ( angle A ) in ( triangle A B C ) in which ( angle B= ) ( mathbf{6 0}, angle boldsymbol{C}=mathbf{4 5}^{mathbf{0}} ) |
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104 | If a triangle ( P Q R ) has been constructed ( operatorname{taking} Q R=6 mathrm{cm}, P Q=3 mathrm{cm} ) and ( P R=4 mathrm{cm}, ) then the correct order of the angle of triangle is A. ( angle P<angle Qangle Qangle Q>angle R ) D. ( angle Pangle R ) |
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105 | Which of the following sets of side lengths form a triangle? A. ( 4 mathrm{m}, 3 mathrm{m}, 11 mathrm{m} ) B. 7 ( mathrm{mm}, 4 mathrm{mm}, 4 mathrm{mm} ) ( c .3 mathrm{cm}, 1.23 mathrm{cm}, 5 mathrm{cm} ) D. 3 ( m, 10 mathrm{m}, 8 mathrm{m} ) |
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106 | The sides of a triangle ( A B C ) are positive integers. The smallest side has length ( l . ) What of the following statements is true? A. The area of ABC is always a rational number B. The area of ABC is always an irrational number c. The perimeter of ABC is an even integer. D. The information provided is not sufficient to conclude any of the statements A, B or C above |
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107 | 58. If I be the incentre of A ABC and ZB = 70° and ZC = 50°. then the magnitude of ZBIC is (1) 130° (2) 60° (3) 120° (4) 105° |
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108 | The angles of triangle are ( x, 5 x, 9 x ) then find the angles of triangle. |
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109 | In an equilateral triangal ( A B C, D ) is a point on side ( mathrm{BC} ) such that ( B D=frac{1}{3} B C ) Prove that ( 9 A D^{2}=7 A B^{2} ) |
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110 | In ( triangle A B C, ) if ( m angle B=90 & A C=10 ) then length of median ( boldsymbol{B} boldsymbol{M}= ) ( A cdot 6 ) B. ( 5 sqrt{2} ) c. D. 8 |
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111 | Find the measures of the missing angle in the given triangle. A ( cdot 30^{circ} ) В. ( 60^{circ} ) ( c cdot 90^{circ} ) D. ( 12^{circ} ) |
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112 | Based on the sides, classify the following triangles |
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113 | Form the given figure, find the values of ( x ) and ( y ) respectively. A ( cdot 47^{circ}, 66^{circ} ) B ( cdot 66^{circ}, 48^{circ} ) ( mathbf{c} cdot 68^{circ}, 47^{circ} ) D. ( 47^{circ}, 68^{text {? }} ) |
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114 | ( Delta A B C ) is an isosceles right triangle with area ( P ).The radius of the circle that passes through the point ( A, B ) and ( C ) is ( A cdot sqrt{P} ) B. ( sqrt{frac{P}{2}} ) c. ( frac{sqrt{P}}{2} ) D. ( sqrt{2 P} ) |
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115 | In each of the following state if the statement is true (T) or false (F): Every acute triangle is equilateral. A. True B. False |
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116 | The largest angle of a triangle is twice the sum of the other two and the smallest one is one fourth of the largest, the angles are A ( cdot 120^{0}, 40^{0}, 20^{0} ) В . ( 120^{0}, 30^{0}, 30^{0} ) c. ( 90^{circ}, 45^{circ}, 45^{circ} ) D. ( 90^{0}, 60^{0}, 30^{0} ) |
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117 | The measure of the third angle of the triangle. ( in degrees ) ( 110^{circ}, 23^{circ},— ) |
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118 | The angles of a triangle are in the ratio ( 2: 3: 4 . ) Find the angles. |
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119 | Show that the following points form an equilateral triangle. ( (sqrt{3}, 2),(0,1) ) and (0,3) | 7 |

120 | The sides of a triangle (in cm) are given below: In which case, the construction of ( triangle ) is |
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121 | Find the length of the longest side of the triangle formed by the line ( 3 x+4 y= ) 12 with the coordinate axes. |
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122 | In the adjacent figure, it is given that ( A B=A C, angle B A C=36^{circ}, angle A D B=45^{circ} ) and ( angle A E C=40^{circ} . ) Find ( angle A C B ) |
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123 | ( A B C ) is an equilateral triangle of side 6 cm. If a circle of radius ( 1 mathrm{cm} ) is moving inside and along the sides of the triangle, then locus of the centre of the circle is an equilateral triangle of side A. ( 5 mathrm{cm} ) B. ( 4 mathrm{cm} ) c. ( (6-2 sqrt{3}) ) ст D. ( (3+sqrt{3}) ) cm |
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124 | As shown in the figure ( boldsymbol{A C}= ) ( boldsymbol{C D}, angle boldsymbol{C A B}-angle boldsymbol{A B C}=mathbf{3 0}^{circ} . ) Then ( angle B A D ) has a measure of: A ( cdot 15^{circ} ) B. 30 ( c cdot 20 ) ( left(22 frac{1}{2}right)^{circ} ) |
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125 | In ( Delta A B C, A B=A C . D, E ) and ( F ) are mid-points of the sides ( B C, C A ) and ( A B ) respectively. then, ( : A D ) is perpendicular to ( boldsymbol{F C} ) If the above statement is true then mention answer as 1 , else mention 0 if false |
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126 | Show that the following points form an isosceles triangle. (2,3),(5,7) and (1,4) | 7 |

127 | If 6,10,14 are the sides of a triangle, then its obtuse angle is A ( cdot 110^{circ} ) B . ( 120^{circ} ) ( mathrm{c} cdot 135^{circ} ) D. ( 115^{circ} ) |
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128 | ( ln Delta mathrm{ABC} angle A=40^{circ} ) and ( angle B=60^{circ} . ) The longest side of triangle ( A B C ) is ( A B ) A. True B. False |
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129 | Assertion If two triangles have same perimeter, then they are congruent. Reason If under a given correspondence, the three sides of one triangle are equal to the three sides of the other triangle, then the two triangles are congruent. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Assertion is incorrect but Reason are correct |
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130 | The ( _{–}-_{-}-_{-}- ) of a triangle is the perpendicular from a vertex to the opposite side. A. centroid B. altitude c. midpoint D. orthocenter |
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131 | n the ( triangle A B C ),we have ( angle A>angle B>angle C ) then determine the shortest and the longest side of the triangle. A. Shortest side is ( A B ) and the longest side is ( B C ) B. Shortest side is ( B C ) and the longest side is ( A B ) C. Shortest side is ( A B ) and the longest side is ( A C ) D. Shortest side is ( A C ) and the longest side is ( B C ) |
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132 | In a ( triangle A B C, ) measure ( angle A=35^{0} ) measure ( angle B=65^{0}, ) find measure ( angle C ) A ( cdot 60^{circ} ) В. ( 70^{circ} ) ( c .80^{circ} ) D. None of these |
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133 | ABCD is a rectangle. If ( A B P ) and ( B C Q ) are equilateral triangle, ( angle P B Q=dots ) A ( cdot 65 ) B. 75 ( c cdot 60 ) D. ( 90^{circ} ) |
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134 | If ( A D, B E ) and ( C F ) are the medians of ( angle ) ABC, then which one of the following statements is correct? ( mathbf{A} cdot(A D+B E+C F)=(A B+B C+C D) ) B ( cdot(A D+B E+C D)>frac{3}{4}(A B+B C+C A) ) ( mathbf{c} cdot(A D+B E+C F)>frac{3}{4}(A B+B C+C A) ) D. ( (A D+B E+C F)=frac{1}{2}(A B+B C+C A) ) |
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135 | ( Delta A B C ) fig. ( 2, angle x+angle y+angle z ) is equals A ( cdot 120^{circ} ) B. ( 180^{text {? }} ) ( c cdot 240 ) D. 360 |
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136 | The sides of a triangle are equal and have equations ( 2 x-y=0,3 x+y=0, x ) ( 3 y+10=0, ) respectively find the equation of three medians of the triangle and verify that they are concurrent |
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137 | Mark the correct alternative of the following. n figure, if ( A B | C D, ) then the values of ( x ) and y are? A. ( x=106, y=307 ) B. ( x=307, y=106 ) c. ( x=107, y=306 ) D. ( x=105, y=308 ) |
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138 | Find the value of ( boldsymbol{X} ) ( mathbf{A} cdot 60^{circ} ) B. ( 70^{circ} ) ( mathbf{c} cdot 80^{circ} ) ( mathbf{D} cdot 90^{circ} ) |
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139 | In an equilateral triangle of side ( 3 sqrt{3} ) find the length of the altitude. | 7 |

140 | The area of an isosceles triangle, each of whose equal sides is ( 13 mathrm{cm} ) and whose base is ( 24 c m ) is ( mathbf{A} cdot 60 mathrm{cm}^{2} ) B. ( 55 mathrm{cm}^{2} ) c. ( 50 mathrm{cm}^{2} ) D. ( 40 mathrm{cm}^{2} ) |
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141 | n figure 1, ( angle P Q R ) is : ( mathbf{A} cdot 40^{circ} ) B ( .50^{circ} ) ( c cdot 30 ) D. 105 |
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142 | A circular park of radius ( 20 m ) is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk to each other. Find the length of the string of each phone. |
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143 | Origin is the centre of circle passing through the vertices of an equilateral triangle whose median is of length ( 3 a ) then equation of the circle is? A ( cdot x^{2}+y^{2}=a^{2} ) B . ( x^{2}+y^{2}=2 a^{2} ) c. ( x^{2}+y^{2}=3 a^{2} ) D. ( x^{2}+y^{2}+4 a^{2} ) |
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144 | In ( triangle A B C, angle A=45^{circ} ) and ( angle B=65^{circ} ) Name the side of the triangle which is shortest |
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145 | f 0 is a point within a quadrilateral ( A B C D, ) prove that ( ; O A+O B+O C+ ) ( O D>A C+B D ) |
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146 | Find the length of altitude through ( A ) of the triangle ( A B C, ) where ( A equiv ) ( (-mathbf{3}, mathbf{0}), boldsymbol{B} equiv(mathbf{4},-mathbf{1}), boldsymbol{C} equiv(mathbf{5}, mathbf{2}) ) |
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147 | ABC is an equilaterial triangle with side ( a . A ) point ( P ) is taken inside ABC. The sum of lengths of perpendiculars from to all the sides is A. greater than altitude from A to BC B. less than altitude form A to BC c. equal to altitude from A to BC D. can’t he determined |
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148 | n ( triangle A B C ) what is sum of the angles a ( + ) ( b+c+d+e+f+g+h+i ? ) ( 4 cdot 360 ) 3.540 ( c cdot 600 ) cannot be determine |
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149 | triangle has three different sides. A. Equilateral B. Isosceles c. Right angled D. Scalene |
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150 | If ( boldsymbol{A}(mathbf{0}, mathbf{3}), boldsymbol{B}(mathbf{0}, mathbf{0}), boldsymbol{C}(mathbf{4} . mathbf{0}) ) be the vertices of a triangle. Then the triangle is A. isosceles B. equilateral c. right angled D. none of these |
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151 | Construct an equilateral triangle, given its side ( =3 ) and justify the construction. |
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152 | In a triangle, the sum of two angles is ( 118^{circ} ) and their difference is ( 32^{circ} ; ) find each angle of the triangle. A ( cdot 75^{circ}, 43^{circ} ) and ( 62^{circ} ) B . ( 70^{circ}, 48^{8} ) and ( 62^{circ} ) c. ( 85^{circ}, 43^{circ} ) and ( 52^{circ} ) D. ( 75^{circ}, 53^{circ} ) and ( 52^{circ} ) |
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153 | If the hypotenuse of a right angled triangle is ( 41 mathrm{cm} ) and the area of the triangle is 180 sq ( c m ), then the difference between the lengths of the triangle must be ( mathbf{A} cdot 22 mathrm{cm} ) B. ( 25 mathrm{cm} ) ( c cdot 27 mathrm{cm} ) D. ( 31 mathrm{cm} ) |
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154 | Prove that each angle of an equilateral triangle is ( 60^{circ} ) |
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155 | Let ( l ) be the length of each equal side of an isosceles triangle. If the length of each equal side is doubled, keeping its height unchanged, then the difference of the squares of bases of the new triangle and the given triangle is ( mathbf{A} cdot mathbf{0} ) B. ( 4 l^{2} ) ( mathrm{c} cdot 9 l^{2} ) D. ( 12 l^{2} ) |
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156 | In any triangle, the side opposite to the larger (greater) angle is longer A. True B. False |
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157 | The measures of angles of a triangle are in the ratio ( 1: 2: 3 . ) Determine the measures of smallest angle of the triangle. |
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158 | Show that the points ( A(1,2), B(1,6), C(1+ ) ( 2 sqrt{3}, 4) ) are vertices of an equilateral triangle. | 7 |

159 | In an isosceles triangle, the vertex angle is ( 50^{circ} . ) What are the base angles of the triangle? |
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160 | In a triangle ( A B C, angle A-angle B=15^{circ} ) and ( angle B-angle C=30^{circ}, ) find ( angle A, angle B ) and ( angle C ) |
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161 | O is any point in the interior of ( Delta A B C ). Prove that ( A B+B C+C A>O A+O B+O C ) |
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162 | PQ is the diameter of given circle and ( angle P R O=35^{circ} . ) Then ( angle R O Q ) equals being the center): A ( cdot 40^{circ} ) B. ( 35^{circ} ) ( c cdot 105^{circ} ) D. 70 |
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163 | If the bisectors of the angles ( angle A B C ) and ( angle A C B ) of a triangle ( A B C ) meet at a point 0, then Prove that ( angle B O C=90^{circ}+ ) ( frac{1}{2} angle B A C ) |
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164 | If all the angles of a triangle measure less than ( 90^{circ} ), then such a triangle is called A. Right angled triangle B. Obtuse angled triangle c. Acute angled triangle D. None of these |
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165 | In an equilateral triangle of side ( 24 mathrm{cm} ) a circle is inscribed touching its sides. Find the area of the remaining portion of the triangle. |
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166 | Number of interior angles formed in the triangle are A . 1 B. 2 ( c .3 ) ( D ) |
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167 | If one angle of a ( Delta ) is equal to the sum of the other two, the triangle is A. isosceles B. equilateral c. right angled D. ordinary |
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168 | In a triangle ( A B C, angle A-angle B=30^{circ} ) and ( angle A ) ( angle C=42^{circ} ; ) find angle ( A ) A ( cdot A=84^{circ} ) B ( cdot A=64 ) C ( cdot A=95 ) D. ( A=92^{circ} ) |
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169 | An isosceles triangle contains three angles that measure ( 40^{circ}, x^{circ}, ) and ( y^{circ} ) Which of the following CANNOT be true? A ( . x=y ) B. ( x=50 ) c. ( x-y=60 ) D. ( x=70 ) E . ( x=100 ) |
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170 | How many angles in the given figure are less than a right angle? ( k ) A .2 B. 3 ( c cdot 4 ) D. 5 |
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171 | The angles of a triangle are in the ratio ( 3: 4: 5 . ) Find the smallest angle. |
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172 | In figure if ( D E | B C ), then find the ratio of ( a r .(triangle A D E) ) and ( a r .(triangle D E C B) . ) Also ( D E=6 mathrm{cm}, B C=12 mathrm{cm} ) |
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173 | Which of the following options is INCORRECT? ( mathbf{A} cdot angle 1=angle 3 ) B . ( angle 1+angle 4+angle 5=180^{circ} ) ( mathbf{c} cdot angle 8=angle 6 ) D. ( angle 1+angle 3=180^{circ} ) |
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174 | If ( C E ) is parallel to ( B D ) in the given figure, then the value of ( x ) will be A . 45 В. 75 ( c .30 ) D. 85 |
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175 | In a ( Delta A B C, angle A B C=angle A C B ) and the bisectors of ( angle A B C ) and ( angle A C B ) intersect at 0 such that ( angle B O C=120^{circ} ) Show that ( angle A=angle B=angle C=60^{circ} ) |
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176 | In ( triangle A B C, ) bisector of ( angle A ) and ( angle B ) intersect at point ( O . ) If ( angle C=70^{circ} ) what is the value of ( angle A O B ? ) |
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177 | Find the unknown angles marked in the following figure. |
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178 | The perimeter of a triangle ( A B C ) is ( 27 mathrm{cm} ) and the ratio between the lengths of its sides is 2: 3: 4 find the sides. A .6,9,12 в. 3,6,9 c. 3,4,5 D. None |
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179 | Show that no triangle has two sides each shorter than its corresponding altitude (from the opposite vertex). | 7 |

180 | Angles of a triangle are in the ratio 4: 6 5. The triangle is : A. an acute angles triangle B. an obtuse angled triangle c. right angled triangle D. isosceles triangle |
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181 | Take any point ( O ) in the interior of a ( triangle P Q R ) Is ( O R+O P>R P ? ) |
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182 | The side of an equilateral triangle is ( 20 sqrt{3} mathrm{cm} . ) The numerical value of the radius of the circle circumscribing the triangle is: ( mathbf{A} cdot 20 mathrm{cm} ) в. ( 20 sqrt{3} mathrm{cm} ) c. ( 20 pi c m ) D. ( frac{20}{pi} ) |
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183 | From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are ( 14 mathrm{cm}, 10 mathrm{cm} ) and ( 6 mathrm{cm} )
The area of the triangle is ( 300 sqrt{m} mathrm{cm}^{2} ) |
7 |

184 | In the given figure ( boldsymbol{alpha} ) and ( boldsymbol{beta} ) are measured in degrees. Which one of the following statements is not correct? ( mathbf{A} cdot beta>alpha ) ( mathbf{B} cdot sec beta=2 ) ( mathbf{C} cdot tan 3 alpha=sqrt{3} ) D ( cdot sin (beta-alpha)=frac{1}{sqrt{2}} ) |
7 |

185 | In the given figure find ( O C ) | 7 |

186 | 67. Let O be the in-centre of a trian- gle ABC and Dbe a point on the side BC of AABC, such that OD I BC. If ZBOD= 15°, then ZABC (1) 75° (3) 150° (2) 45° (4) 90° |
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187 | Two angles of a triangle measure ( 52^{circ} ) and ( 72^{circ} . ) Find the measure of the third angle of the triangle. A ( .36^{circ} ) B . 46 ( c cdot 56^{circ} ) D. ( 66^{circ} ) |
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188 | In each case; given below, find the value of ( x ) in terms of ( a, b ) and ( c ) A ( . x=180^{circ}-a-b+c ) B . ( x=180^{circ}+b+a+c ) c. ( x=180^{circ}+b-a-c ) D. ( x=180^{circ}+a+b-c ) |
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189 | A triangle cannot have more than right angle(s). A. one B. two c. three D. zero |
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190 | In the figure the sides ( B C, C A ) and ( A B ) of a ( triangle A B C ) have been produced to ( D, E ) and ( F ) respectively. If ( angle A C D=105^{circ} ) and ( angle E A F=45^{circ}, ) find all the angles of the ( triangle A B C ) |
7 |

191 | AD is the bisector of ( angle A ) of ( Delta A B C, A C=4.2 c m, D C= ) ( 6 c m, B C=10 c m, ) then ( A B ) is: ( mathbf{A} cdot 2.8 mathrm{cm} ) B. 3 cm ( mathrm{c} .3 .5 mathrm{cm} ) D. none of these |
7 |

192 | 5. In Fig, determine ZP+ 2Q+ZR+ S+ZT. 54 p 10 |
7 |

193 | For ( Delta A B C, ) find the measure of ( angle A C D ) | 7 |

194 | ( angle C E D ) | 7 |

195 | If the triangle ( A B C ) in the question 7 above is revolved 7 above is resolved the side ( 5 mathrm{cm}, ) then find the volume of the solid so obtained Find also ratio of the volumes of the two solids obtained in Questions 7 and 8 |
7 |

196 | Find the length of the altitude of the hypotenuse. ( A cdot 5.12 ) 3. 5.25 .5 .34 4 5.6 |
7 |

197 | If the equal sides of an isosceles triangle ( A B C ) are produced, prove that the exterior angles so formed are obtuse,say ext ( angle B, ) and find ( e x t angle B- ) ( angle A ) |
7 |

198 | Find the values of ( angle a angle b ) in the figure given below. |
7 |

199 | If the bisector of the exterior vertical angle of a triangle is parallel to the base, show that the triangle is isosceles. |
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200 | If ( A, B ) and ( C ) are interior angles of a triangle ( A B C, ) then show that tan ( left(frac{boldsymbol{A}+boldsymbol{B}}{mathbf{2}}right)=cot frac{boldsymbol{C}}{2} ) |
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201 | How many triangles can be drawn having its angles as ( 53^{circ}, 64^{circ} ) and ( 63^{circ} ? ) ( mathbf{A} cdot mathbf{1} ) B. 2 c. None D. More than 2 |
7 |

202 | ( A B C ) is an isosceles triangle in which ( A B ) ( =A C A ) circle through ( B ) touches side ( A C ) at its mid point ( mathrm{D} ) and intersects ( mathrm{AB} ) at ( P, ) then ( A P ) will be- ( A cdot 2 A D ) B ( cdot frac{1}{2} A B ) c. ( frac{1}{4} A B ) D. ( frac{1}{2} A C ) |
7 |

203 | If two vertices of an isosceles triangle ( operatorname{are}(2,0) ) and (2,5) and length of the equal sides is 3 then the third vertex is A ( .(2,6) &(-5,3) ) B. (8,3)( &(5,1) ) ( ^{mathbf{C}} cdotleft(2 pm frac{sqrt{11}}{2}, frac{5}{2}right) ) D. ( left(3 pm frac{sqrt{14}}{2}, frac{7}{2}right) ) |
7 |

204 | Find the vertex of the median ( boldsymbol{M}_{mathbf{1}} ) ( mathbf{A} cdot A ) B. ( B ) ( c cdot C ) ( D . D ) |
7 |

205 | In figure ( -1, ) which of the following statement is true? ( mathbf{A} cdot angle B=angle C ) B. ( angle B ) is the greatest angle in triangle ( mathrm{c} . angle B ) is the smallest angle in triangle D. ( angle A ) is the smallest angle in triangle |
7 |

206 | If length of the largest side of a triangle is ( 12 mathrm{cm} ) then other two sides of triangle can be : ( A cdot 4.8 mathrm{cm}, 8.2 mathrm{cm} ) B. 3.2 ( mathrm{cm}, 7.8 mathrm{cm} ) c. ( 6.4 mathrm{cm}, 2.8 mathrm{cm} ) D. ( 7.6 mathrm{cm}, 3.4 mathrm{cm} ) |
7 |

207 | The angles of a triangle are in the ratio of ( 1: 2: 3 . ) Find the measure of each angle of the triangle A ( cdot 30^{circ}, 60^{circ}, 90^{circ} ) B . ( 20^{circ}, 60^{circ}, 90^{circ} ) c. ( 30^{circ}, 30^{circ}, 90^{circ} ) D. None of these |
7 |

208 | Prove that the median from the vertex of an isosceles triangle is the bisector of vertical angle. |
7 |

209 | Two sides of a triangle are of lengths 5 ( mathrm{cm} ) and ( 1.5 mathrm{cm}, ) then the length of the third side of the triangle cannot be ( mathbf{A} cdot 3.6 mathrm{cm} ) B. ( 4.1 mathrm{cm} ) c. ( 3.8 mathrm{cm} ) D. ( 3.4 mathrm{cm} ) |
7 |

210 | State the property that is used in each of the following statements? If ( angle mathbf{4}=angle mathbf{5}=mathbf{1 8 0}^{circ} ) then ( boldsymbol{a} | boldsymbol{b} ) |
7 |

211 | 0 is a point that lies in the interior of ( Delta A B C . ) Then ( 2(O A-O B-O C)> ) Perimeter of ( Delta A B C ) A. True B. False |
7 |

212 | ( ln Delta A B C, ) if ( A B>B C ) then : ( mathbf{A} cdot angle Cangle A ) ( mathbf{D} cdot angle A=angle B ) |
7 |

213 | The height of an equilateral triangle of side ‘a’ is given by A ( cdot frac{a sqrt{2}}{2} ) B. ( frac{a sqrt{3}}{2} ) c. ( frac{a sqrt{3}}{4} ) D. ( frac{a sqrt{2}}{3} ) |
7 |

214 | ( A B C ) is an isosceles triangle such that ( A B=A C . D ) is the mid point of ( A C . A ) circle is drawn taking ( B D ) as diameter which intersects ( A B ) at point ( E ).then ( boldsymbol{A C}=mathbf{3 A E} ) A. True B. False |
7 |

215 | In a right-angled triangle ( A B C ) with ( angle C=90^{circ} ) and ( angle A=2 angle B, angle B ) is A ( cdot 15^{circ} ) В. ( 60^{circ} ) ( c cdot 45^{circ} ) D. ( 30^{circ} ) |
7 |

216 | The incenter of ( Delta A B C ) with vertices ( A(0,0,4), B(3,0,4), C(0,4,4) ) is A ( .(1,1,1) ) в. (1,1,2) c. (1,1,3) D. (1,1,4) |
7 |

217 | The sides of a right triangle are 9,12 and ( 15 mathrm{cm} ) long. Find the sum of the squares of the medians. A. ( 327.5 mathrm{cm} ) B . ( 332.5 mathrm{cm} ) c. ( 337.5 mathrm{cm} ) D. ( 322.5 mathrm{cm} ) |
7 |

218 | In an isosceles ( triangle A B C, ) if ( A B=A C ) and ( D ) is a point on ( B C, ) then prove that ( A B^{2}-A D^{2}=B D . C D ) |
7 |

219 | Identify the triangle as equiangular acute, obtuse or right. Answer: Right angled triangle Mark answer as 1 if true else 0 if false ( (i) ) |
7 |

220 | The medians of a right triangle which are drawn from the vertices of the acute angles are 5 and ( sqrt{4} 0 . ) The value of the hypotenuse is: A . 10 в. ( 2 sqrt{40} ) ( c cdot sqrt{13} ) D. ( 2 sqrt{13} ) E. none of these |
7 |

221 | The angles in a right angled isosceles triangle are: A ( cdot 60^{circ}, 60^{circ}, 60^{circ} ) B . ( 90^{circ}, 60^{circ}, 30^{circ} ) c. ( 90^{circ}, 45^{circ}, 45^{circ} ) D . ( 70^{circ}, 50^{circ}, 60^{circ} ) |
7 |

222 | If each side of an equilateral triangle is doubled then its angle will A. become half B. be doubled c. be tripled D. remain same |
7 |

223 | In an acute angled triangle ( A B C, A P ) is the altitude. Circle drawn with AP as its diameter cuts the sides ( A B ) and ( A C ) at ( D ) and ( mathrm{E} ), respectively, then length DE is equal to A ( cdot frac{Delta}{2 R} ) в. ( frac{Delta}{3 R} ) c. ( frac{Delta}{4 R} ) D. ( frac{Delta}{R} ) |
7 |

224 | The number of values of b for which there is an isosceles triangle with sides of lengths ( b+5,3 b-2 ) and ( 6-b ) is/are A. B. ( c cdot 2 ) D. 3 |
7 |

225 | ( A M ) is a median of a triangle ( A B C . ) Is ( A B+B C+C A>2 A M ? ) (Consider the sides of triangles ( Delta A B M text { and } Delta A M C) ) A. True B. False |
7 |

226 | In a triangle the measured of the angles are ( x, x+20, ) and ( 2 x . ) What is the value of x? |
7 |

227 | ( boldsymbol{E} ) and ( boldsymbol{F} ) are the points on the side ( boldsymbol{P Q} ) and ( P R ) respectively of ( triangle P Q R ) For each of the following cases, state that ( boldsymbol{E} boldsymbol{F} | ) ( Q R ) If True type 1 and for False type 0 ( boldsymbol{P E}=mathbf{4} boldsymbol{c m}, boldsymbol{Q} boldsymbol{E}=mathbf{4 . 5} boldsymbol{c m}, boldsymbol{P} boldsymbol{F}= ) ( 8 c m ) and ( R F=9 c m ) |
7 |

228 | In the given isosceles triangle, side ( B C=14 c m ) and side ( A B=1 frac{1}{2} l(B C) ) Find the perimeter of the given triangle |
7 |

229 | In a triangle ( A B C, angle A=90^{circ}, ) and ( A D ) is the altitude. Complete the relation ( frac{B D}{B A}=frac{A B}{D B}-left(frac{ldots ldots .}{A B times B D}right) ) |
7 |

230 | In ( triangle A B C, D ) is a point on ( B C ) such that ( A B=A D=B D=D C, ) then: ( angle A D C: angle C=3: 1 ) A. True B. False |
7 |

231 | In a triangle, the largest angle is ten times the smallest and the remaining angle is the square of the smallest. The largest angle of the triangle is A ( .80^{circ} ) B . ( 100^{circ} ) ( c cdot 120^{circ} ) D. ( 90^{circ} ) |
7 |

232 | It is not possible to construct a triangle when its sides are: A. ( 8.3 mathrm{cm}, 3.4 mathrm{cm}, 6.1 mathrm{cm} ) B. ( 5.4 mathrm{cm}, 2.3 mathrm{cm}, 3.1 mathrm{cm} ) c. ( 6 mathrm{cm}, 7 mathrm{cm}, 10 mathrm{cm} ) D. 3 cm, 5 cm, 5 cm |
7 |

233 | In a right angled triangle if an angle measures then ( 35^{0} ) the measure of other angle is A ( .65^{circ} ) B. 55 c. ( 45^{circ} ) D. 30 |
7 |

234 | In the given figure, if AL is the bisector of ( Delta B A C, ) then ( A B ) is ( A .7 c m ) B. ( 10 mathrm{cm} ) ( c .15 c m ) D. ( 22.50 mathrm{cm} ) |
7 |

235 | The base angles of an isosceles triangle is ( 50^{circ} . ) The size of vertical angle is A ( .55^{circ} ) B. ( 35^{circ} ) ( c cdot 70^{circ} ) D. ( 80^{circ} ) |
7 |

236 | In the given fig ( A D ) divides ( angle B A C ) in the ratio 1: 3 and ( A D=D B ) Determine the value of ( x ) |
7 |

237 | If two medians of a triangle are equal in length, then the new triangle formed as a result of the medians is: A. right angled but not isosceles B. isosceles but not right angle c. right angled isosceles D. equilateral |
7 |

238 | Measure of angle ( angle A C D ) in the given figure is: A ( .130^{circ} ) B. 120 ( c cdot 150 ) D. ( 115^{circ} ) |
7 |

239 | Suppose that the lines which bisect the exterior angles at ( B ) and ( C ) of ( Delta A B C ) meet at ( D . ) Then find ( angle B D C ) |
7 |

240 | Find the altitude of an equilateral triangle of side ( 5 sqrt{3} c m ) A ( .7 .5 mathrm{cm} ) в. ( 12.5 mathrm{cm} ) ( mathrm{c} .9 .5 mathrm{cm} ) D. ( 8.5 mathrm{cm} ) |
7 |

241 | The lengths of two sides of a triangle are ( 3 mathrm{cm} ) and ( 4 mathrm{cm} . ) Which of the following, can be the length of third side to form a triangle? A . ( 0.5 mathrm{cm} ) B. ( 5 mathrm{cm} ) ( c .8 mathrm{cm} ) D. ( 10 mathrm{cm} ) |
7 |

242 | ( ln ) a ( Delta P Q R, ) if ( P Q=P R ) and ( angle Q ) is twice that of ( angle P, ) then ( angle Q= ) A .72 B. 36 c. ( 144^{circ} ) D. ( 108^{circ} ) |
7 |

243 | Find ( x, ) if the angles of a triangle have measures ( left(x+40^{0}right),left(2 x+20^{0}right) ) and ( 3 x ) also state which type of triangle is this. A . ( x=60^{circ} ) and Equilateral triangle B. ( x=20^{circ} ) and Scalene triangle C . ( x=20^{circ} ) and Equilateral triangle D. ( x=40^{circ} ) and Scalene triangle |
7 |

244 | ( A B C D ) is a quadrilateral ( mathbf{s} boldsymbol{A B}+boldsymbol{B C}+boldsymbol{C D}+boldsymbol{D A}>boldsymbol{A C}+boldsymbol{B D} ) A. True 3. Falss |
7 |

245 | in the given figure if DEllAC and DCIIAP then which of the following is ture A ( cdot operatorname{BE}(mathrm{AD}+mathrm{CP})=mathrm{BE}^{2} ) B. ( mathrm{BE} times mathrm{CP}=mathrm{EC} times mathrm{BC} ) c. ( mathrm{BC} times mathrm{CP}=mathrm{EC} times mathrm{BC} ) D. ( B D times D E times=B E^{2} ) |
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246 | Which is the greatest side in the following triangle? ( angle boldsymbol{A}: angle boldsymbol{B}: angle boldsymbol{C}=mathbf{4}: mathbf{5}: mathbf{6} ) ( mathbf{A} cdot A B ) в. ( B C ) ( c . A C ) D. cannot be determined |
7 |

247 | Prove that external angle is sum of the opposite interior angle. |
7 |

248 | In the figure find the values of ( x ) and ( y ) | 7 |

249 | Using the information, given in each of the following figures, find the valuesof ( a ) ( [text { Given }: boldsymbol{C} boldsymbol{E}=boldsymbol{A C}] ) A . ( 136^{circ} ) B. ( 124^{circ} ) ( c cdot 110^{circ} ) D. none of the above |
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250 | An altitude and a median drawn from the same vertex of a triangle divide the angle at that vertex into.three equal parts. Prove that the angles of that triangle are equal to ( 30^{circ}, 60^{circ}, ) and ( 90^{circ} ) |
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251 | In the given triangle ( A B C, ) find the measure of ( angle boldsymbol{A B C} ) |
7 |

252 | A circle of radius ( 10 mathrm{cm} ) has its centre at the vertex ( C ) of an equilateral triangle ABC and passes through the other two vertices. The side AC extended through C intersects the circle at D. The number of degrees of angle ADB is: A ( cdot 15^{circ} ) B . ( 30^{circ} ) ( c cdot 60^{circ} ) D. ( 90^{circ} ) E ( .120^{circ} ) |
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253 | ( ln a Delta A B C, ) it is given that ( A B=A C ) and the bisectors of ( angle B ) and ( angle C ) intersect at ( 0 . ) If ( mathrm{M} ) is a point on ( mathrm{BO} ) produced, prove that ( angle M O C=angle A B C ) |
7 |

254 | If three angles of a triangle are in the ratio ( 2: 3: 5, ) determine three angles. | 7 |

255 | In an isosceles triangle ( A B C ), with ( A B=A C ), the bisectors of ( angle B ) and ( angle C ) interest each other at ( O ) join ( A ) to ( O ) show that: ( (i) O B=O C ) (ii) ( A O ) bisects ( angle A ) |
7 |

256 | Measure of ( angle A ) in ( Delta A B C ) is ( A cdot 90^{circ} ) В. ( 99.3^{circ} ) ( c cdot 100.3^{circ} ) ( 800.7^{circ} ) |
7 |

257 | n fig sides QP and RQ of ( Delta ) PQR are produced to the points ( mathrm{S} ) and ( mathrm{T} ) respectively. If ( angle S P R=105^{circ} angle P Q T= ) ( 110^{circ} ) then find ( angle P R Q ) ( A cdot 35 ) B. ( 70^{circ} ) ( c .105 ) 0.140 |
7 |

258 | In the figure above, point ( A ) and ( B ) lie on the circle with center ( O . ) If ( x=80, ) what is the value of ( z ? ) A . ( 80^{circ} ) B. ( 60^{circ} ) ( c cdot 50^{circ} ) D. ( 40^{circ} ) E .10 |
7 |

259 | ( P Q R S ) is a square and ( Delta T S R ) is ar isosceles triangle with ( T S=T R ) Prove that ( boldsymbol{P T}=boldsymbol{Q} boldsymbol{T} ) |
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260 | In the given figure, ( A M perp B C ) and ( A N ) is the bisector of ( angle A ). Then ( angle M A N ) is A ( cdot 32 frac{1}{2} ) B . ( 16 frac{1}{2} ) ( c cdot 16^{0} ) ( D cdot 32^{0} ) |
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261 | In the figure below, AL is perpendicular to BC and CM is perpendicular to AB. If ( C L=A L=2 B L, ) find ( $ $ backslash ) dfrac ( {text { MC }} ) ( [mathrm{AM}} ) ( A ) B. ( c ) ‘. cannot be determine |
7 |

262 | ( A B C ) is a right-angle triangle, right angled at A. A circle is inscribed in it. The lengths of the two sides containing the right angle are ( 6 mathrm{cm} ) and ( 8 mathrm{cm} ) then radius of the circle is : ( A cdot 3 mathrm{cm} ) B. ( 2 mathrm{cm} ) ( c cdot 4 mathrm{cm} ) D. ( 8 mathrm{cm} ) |
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263 | What is the largest angle of the triangle? ( A cdot x ) B. ( c cdot z ) ( D ) |
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264 | Name the following triangle in two different ways.(you mayjudge the nature of the angle by observation) | 7 |

265 | The mean of 10 observations is ( 16.3 . ) If one observation is registered as 32 instead of 23 , then new mean is A . 14.8 B. 15.4 ( c cdot 16 . ) D. 16.6 |
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266 | Ratio of angle in 5: 3: 1 find the angle. | 7 |

267 | In the given figure, ( angle P R Q=angle P Q R ) then prove that ( angle P Q S=angle P R T ) |
7 |

268 | Show that in a right-angled triangle, the hypotenuse is the longest side. | 7 |

269 | The number of triangles with any three of the length 1,4,6 and ( 8 mathrm{cm} ) as sides is: A . 4 B. 2 c. 1 ( D ) |
7 |

270 | How many medians are there in a triangle ( P Q R ? ) 4 B. 2 ( c ) ( D ) |
7 |

271 | Two line segments ( A B ) and ( A C ) include an angle of ( 60^{0} ) where ( A B=5 mathrm{cm} ) and ( A C ) ( =7 mathrm{cm} . ) Locate points ( mathrm{P} ) and ( mathrm{Q} ) on ( mathrm{AB} ) and ( A C, ) respectively such that ( A P=frac{3}{4} ) ( A B ) and ( A Q=frac{1}{4} A C . ) Join ( P ) and ( Q ) and measure the length PQ. A. ( 3.25 mathrm{cm} ) B. ( 4.25 mathrm{cm} ) ( c .5 .25 mathrm{cm} ) D. ( 6.25 mathrm{cm} ) |
7 |

272 | From the given figure, find ( x ) | 7 |

273 | Pis a point inside ( Delta A B C . ) If ( angle P B A= ) ( mathbf{2 0}^{circ}, angle boldsymbol{B} boldsymbol{A} boldsymbol{C}=mathbf{5 0}^{circ}, ) and ( angle boldsymbol{P C A}=mathbf{3 5}^{circ} ) then the measure of ( angle B P C ) is ( 4 cdot 65^{circ} ) B. ( 75^{circ} ) ( c cdot 90 ) D. 105 |
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274 | Can a triangle have two obtuse angles? If True enter 1 , else enter 0 |
7 |

275 | What is the number of distinct triangles with integral valued sides and perimeter as ( 14 ? ) | 7 |

276 | If ( A, B, C ) are the angles of a triangle, show that ( frac{cos A cos C+cos (A+B) cos (B+C)}{cos A sin C-sin (A+B) cos (B+C)} ) ( cot C ) |
7 |

277 | ( A B C ) and ( A B D ) are two triangles on the same base ( A B . ) If line-segment ( C D ) is bisected by ( A B ) at ( O, ) show ( operatorname{that} boldsymbol{a r}(boldsymbol{A B C})=boldsymbol{a r}(boldsymbol{A B D}) ) |
7 |

278 | ( mathrm{n} Delta A B C, mathrm{AD} ) bisects ( angle B A C ) and ( mathrm{AD}= ) DC. If ( angle A D B=100^{circ} ), then find ( angle A B D ). ( A cdot 30 ) в. 45 ( c cdot 60 ) D. 90 |
7 |

279 | In an equilateral triangle ( A B C, D ) is a point on side ( B C ) such that ( B D=frac{1}{3} ) Prove that ( 9 A D^{2}=7 A B^{2} ) |
7 |

280 | ( A B C ) is an isosceles triangle with vertex at ( A ) and ( P ) is any point inside the triangle. If the rectangle contained by perpendicular from ( boldsymbol{P} ) to sides ( boldsymbol{A B} ) and ( A C ) is equal to square of the perpendicular from ( boldsymbol{P} ) to base ( boldsymbol{B} boldsymbol{C}, ) then prove that the locus of ( boldsymbol{P} ) is a circle. |
7 |

281 | State true or false: Difference of any two sides of a triangle is equal to the third side. A. True B. False |
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282 | If the ratio of the angles of a triangle is 2: 3: 5 then angles are A ( cdot 36^{circ}, 54^{circ}, 90^{circ} ) В . ( 18^{circ}, 36^{circ}, 126^{circ} ) c. ( 20^{circ}, 60^{circ}, 180^{circ} ) D. ( 18^{circ}, 60^{circ}, 102^{circ} ) |
7 |

283 | Show that ( A(6,4), B(5,-2) ) and ( C(7,-2) ) are the vertices of an isosceles triangle. Also, find the length of the median through ( A ) |
7 |

284 | Assertion Show that the points ( (boldsymbol{a}, boldsymbol{a}),(-boldsymbol{a},-boldsymbol{a}) ) and ( (-sqrt{3} a, sqrt{3} a) ) are the vertices of an equilateral triangle. Reason Using the distance formula we can show that the sides are equal. A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect |
7 |

285 | In a triangle ( mathrm{ABC}, angle A=110^{circ} ) and ( A B=A C . ) Find ( angle B ) and ( angle C ) |
7 |

286 | If (-4,0),(0,3),(0,-3) are the vertices of a triangle, then find the shape of the triangle. A. isosceles B. equilateral c. scalene D. None of these |
7 |

287 | The length of vector AG is? A ( . sqrt{17} ) в. ( frac{sqrt{51}}{3} ) c. ( frac{sqrt{51}}{9} ) D. ( frac{sqrt{59}}{4} ) |
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288 | If the altitudes of a triangle be 3,4,6 then find its in-radius. |
7 |

289 | From a point 0 in the interior of a ( Delta A B C, ) perpendiculars ( 0 D, O E, & ) OF are drawn to the sides BC, CA & AB respectively. Prove that [i] ( A F^{2}+B D^{2}+C E^{2}=O A^{2}+ ) ( O B^{2}+O C^{2}-O D^{2}-O E^{2}-O F^{2} ) [ii] ( A F^{2}+B D^{2}+C E^{2}=A E^{2}+ ) ( C D^{2}+B F^{2} ) |
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290 | How do you know the triangle is right angled? A. The triangle is right angled when the three sides of a triangle make ( a^{2}+b^{2}=c^{2} ) B. The triangle is right angled when the three sides of a triangle do not make ( a^{2}+b^{2}=c^{2} ) C. The triangle is not right angled when the three sides of a triangle make ( a^{2}+b^{2}=c^{2} ) D. The three sides of a triangle are all same. |
7 |

291 | In ( Delta A B C, angle A=120, B C+C A=20 ) ( A B+B C=21, ) then ( mathbf{A} cdot A B>A C ) B. AB c. ( triangle A B C ) is isosceles D. Area of ( Delta A B C=14 sqrt{3} ) |
7 |

292 | n figure, if lines ( mathrm{PQ} ) and ( mathrm{RS} ) intersect at point ( mathrm{T} ), such that ( angle boldsymbol{P} boldsymbol{R} boldsymbol{T}= ) ( 40^{circ}, angle R P T=95^{circ} ) and ( angle T S Q=75^{circ} ) find ( angle S Q T ). ( 4 cdot 20 ) 3.60 ( c cdot 30 ) ( D ) |
7 |

293 | In ( Delta A B C, angle A=43^{circ} ) and ( angle C=70^{circ} ) What is the measure of ( angle B ? ) ( mathbf{A} cdot 63^{circ} ) B. ( 65^{circ} ) ( c cdot 66^{circ} ) D. ( 67^{circ} ) |
7 |

294 | Prove that in an equilateral triangle, three time the square of a side is equal to four time the square of its altitude. | 7 |

295 | Measure of ( angle B ) and ( angle C ) are ( mathbf{A} cdot 75^{circ}, 85 ) B ( cdot 75^{circ}, 75 ) ( mathbf{c} cdot 55^{circ}, 55^{circ} ) D. ( 65^{circ}, 65^{circ} ) |
7 |

296 | Prove that ( angle B O C=90+frac{1}{2} angle B A C ) | 7 |

297 | If a ( triangle A B C, ) the bisectors ( angle B ) and ( angle C ) intersect at ( O . ) Prove that ( angle B O C= ) ( mathbf{9 0}^{circ}+frac{mathbf{1}}{mathbf{2}} angle boldsymbol{A} ) |
7 |

298 | In Fig., the length (in ( mathrm{cm} ) ) of each side has been indicated along the side. State for each triangle whether it is scalene, isosceles or equilateral: |
7 |

299 | In the adjoining figure, ( A B C ) is triangle in which ( A D ) is the bisector of ( angle A . ) If ( A D perp B C, ) show that ( Delta A B C ) is isosceles. |
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300 | The side of an equilateral triangle is ( 4 sqrt{3} mathrm{cm} . ) The length of a perpendicular drawn from any vertex to the opposite side will be A. ( 4 mathrm{cm} ) B. 6 ст ( c .8 c m ) D. ( 9 mathrm{cm} ) |
7 |

301 | If ( triangle A B C ) has differnence side length ( a, b, c ) and ( a^{2}, b^{2}, c^{2} ) as side will again form another ( triangle P Q R, ) then ( triangle A B C ) will always be A. Acute angle triangle only B. Obtuse angle triangle only c. Something Acute or something obtuse depending on value of ( a, b ) and ( c ) D. None of these |
7 |

302 | Sum of all the three interior angles of a triangle is equal to A ( .360^{circ} ) B . ( 120^{circ} ) c. ( 180^{circ} ) D. ( 90^{circ} ) |
7 |

303 | 54. I is the incentre of A ABC, LABC = 60° and ZACB = 50°. Then Z BIC is : (1) 55° (2) 125° (3) 70° (4) 65° |
7 |

304 | Sum of any two sides of a triangle is than the third side. A. Greater B. Lesser c. Equal D. May be greater or lesser |
7 |

305 | In ( Delta A B C, ) if ( angle A=50^{circ} ) and ( angle B=60^{circ} ) then the greatest side is : ( A cdot A B ) B. BC c. АС D. cannot say |
7 |

306 | Find the angles ( x ) and ( y ) in the adjoining figure. |
7 |

307 | ( frac{sin 2 x}{2 cos x}=tan x ? ) A. True B. False |
7 |

308 | If the points ( (0,0),(3, sqrt{3}),(p, q) ) form an equilateral triangle and ( boldsymbol{q}_{1}, boldsymbol{q}_{2} ) are the two values of ( boldsymbol{q} ) then ( boldsymbol{q}_{1}+boldsymbol{q}_{2}=? ) A ( cdot 2 sqrt{3} ) B. ( sqrt{3} ) ( c cdot-sqrt{3} ) D. |
7 |

309 | | vidnu nas decided to create a triangular flower bed border. He plans to use 3 pieces of rectangular wooden plates with lengths 4,5 and 6 feet, as shown in the figure. Manu plans to cut the 3 pieces of plate for the flower bed border from a single |
7 |

310 | In the given figure, ( frac{P K}{K S}=frac{P T}{T R} ) and ( angle P K T=angle P R S . ) Prove that ( Delta P S R ) is an isosceles triangle. |
7 |

311 | If ( S ) is any point in the interior of ( Delta P Q R ) prove that ( (boldsymbol{S} boldsymbol{Q}+boldsymbol{S} boldsymbol{R})<(boldsymbol{P} boldsymbol{Q}+boldsymbol{P} boldsymbol{R}) ) | 7 |

312 | Using triangle inequality theorem check whether the given side lengths ( boldsymbol{a}=mathbf{4}, boldsymbol{b}=mathbf{5} ) and ( boldsymbol{c}=mathbf{8} ) will form a triangle or not |
7 |

313 | An exterior angle of a triangle is ( 105^{circ} ) and its two interior opposite angles are equal. Each of these equal angles is A. ( _{37} frac{1^{0}}{2} ) в. ( _{52} frac{1^{0}}{2} ) c. ( _{72} frac{1^{0}}{2} ) D. 75 |
7 |

314 | In the figure given below, measure of ( angle A B C ) is A . ( 60^{circ} ) B. 70 ( c .80 ) D. 50 |
7 |

315 | If ( G ) is centroid and ( A D, B E, C F ) are three medians of ABC with area ( 72 mathrm{cm}^{2} ), then the area of BDG is A ( cdot 12 ~ c m^{2} ) B. ( 16 mathrm{cm}^{2} ) c. ( 24 mathrm{cm}^{2} ) D. ( 8 mathrm{cm}^{2} ) |
7 |

316 | Area of ( Delta A B C(text { in sq units }) ) is? A .24 B. ( 8 sqrt{6} ) ( c cdot 4 sqrt{6} ) D. None of these |
7 |

317 | How many isosceles triangles are there with ( 40^{circ} ) as one of the three angles? ( mathbf{A} cdot mathbf{0} ) B. ( c cdot 2 ) D. 3 |
7 |

318 | Which is the smallest side in the following triangle? ( angle P: angle Q: angle R=1: 2: 3 ) A. ( P Q ) в. ( Q R ) c. ( P R ) D. cannot be determined |
7 |

319 | In a circle with center ( 0, ) chords ( A B ) and CD are of length ( 5 mathrm{cm} ) and ( 6 mathrm{cm} ) respectively and subtend angle ( x^{circ} ) and ( y^{circ} ) at center of circle respectively then A ( cdot x^{circ}=y^{circ} ) В . ( x^{circ}y^{circ} ) D. None of the above |
7 |

320 | Which of the following will be the angles of a triangle? A ( cdot 35^{circ}, 45^{circ}, 90^{circ} ) B . ( 26^{circ}, 58^{circ}, 96^{circ} ) ( mathbf{c} cdot 38^{circ}, 56^{circ}, 96^{circ} ) D . ( 30^{circ}, 55^{circ}, 90^{circ} ) |
7 |

321 | Let ( vec{a}, vec{b}, vec{c} ) be position vectors of three vertices of triangle ( A B C, ) find the area of triangle ( A B C ) | 7 |

322 | In a ( triangle A B C, ) if ( 2 angle A=3 angle B=6 angle C ) calculate the measures of ( angle B ) (in degrees) |
7 |

323 | The angles of triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is ( 15^{circ}, ) find the three angles. |
7 |

324 | ( A B C ) is a triangle right-angled at ( B ) and ( D ) is a point on ( B C ) produced ( (B D>B C), ) such that ( B D=2 D C ) Which one of the following is correct? A. ( A C^{2}=A D^{2}-3 C D^{2} ) B. ( A C^{2}=A D^{2}-2 C D^{2} ) c. ( A C^{2}=A D^{2}-4 C D^{2} ) D. ( A C^{2}=A D^{2}-5 C D^{2} ) |
7 |

325 | The lengths of two sides of a triangle are ( 7 mathrm{cm} ) and ( 10 mathrm{cm} . ) What is the possible value range of the third side? A. ( 3 mathrm{cm}< ) third side ( <10 mathrm{cm} ) B. ( 7 mathrm{cm}< ) third side ( <10 mathrm{cm} ) ( mathrm{c} cdot 3 mathrm{cm}< ) third side ( <17 mathrm{cm} ) D. ( 7 mathrm{cm}< ) third side |
7 |

326 | In ( Delta A B C, ) if ( angle A=35^{circ} ) and ( angle B=65^{circ} ) then the longest side of the triangle is : A . AC B. AB c. вс D. None of these |
7 |

327 | o Prove: ( -frac{boldsymbol{A} boldsymbol{M}}{boldsymbol{A B}}=frac{boldsymbol{A} boldsymbol{N}}{boldsymbol{A D}} ) | 7 |

328 | How many triangles can be drawn having its angles as ( 45^{0}, 64^{0} ) and ( 72^{0} ? ) ( mathbf{A} cdot mathbf{1} ) B . 2 c. More than 2 D. None |
7 |

329 | The triangle formed by ( B C= ) ( 5 c m, A C=3 c m, A B=5.8 c m ) is: A. a right angled ( Delta ) B. an isosceles ( Delta ) c. an equilateral ( Delta ) D. a scalene ( Delta ) |
7 |

330 | Find the exterior angle. A . ( 31^{circ} ) B. ( 32^{circ} ) ( mathbf{c} cdot 33^{circ} ) D. 34 |
7 |

331 | ( A, B, C ) are the three angles of a triangle ( . ) if ( boldsymbol{A}-boldsymbol{B}=mathbf{1 5}^{circ}, boldsymbol{B}-boldsymbol{C}=mathbf{3 0}^{circ} ) find ( angle boldsymbol{A}, angle boldsymbol{B}, angle boldsymbol{C} ) |
7 |

332 | In the given figure, ABCD is a parallelogram in which ( angle B D C=45^{circ} ) and ( angle B A D=75^{circ} . ) Then, ( angle C B D=? ) ( A cdot 150 ) 3. 105 ( c cdot 60^{circ} ) ( D .75 ) |
7 |

333 | One vertex of the equilateral triangle with centroid at the origin and one side as ( boldsymbol{x}+boldsymbol{y}-boldsymbol{2}=mathbf{0} ) is? A ( cdot(-1,-1) ) в. (2,2) c. (-2,-2) D. None of these |
7 |

334 | Fill in the blanks in the following so that each of the following statements is true. ( ln a Delta B C ) if ( angle A=angle C, ) then ( A B=dots ) | 7 |

335 | In the given figure (not drawn to scale), ( A B C D ) is a parallelogram, ( A D F ) is an isosceles triangle with ( boldsymbol{A} boldsymbol{D}=boldsymbol{A} boldsymbol{F} ) ( F A B ) and ( E D C ) are straight lines. Find ( boldsymbol{y} ) A . 112 в. 102 ( c .132 ) D. 11 |
7 |

336 | ( ln Delta A B C, ) if ( A B=B C ) and ( angle B= ) ( 80^{circ}, ) then ( angle C= ) A . ( 50^{circ} ) B. 100 ( c cdot 130^{circ} ) D. None |
7 |

337 | n given figure the measure of ( angle A+ ) ( angle B+angle C+angle D+angle E+angle F ) is ? ( A cdot 120 ) 3.720 ( c cdot 360 ) ) .540 |
7 |

338 | ( ln ) a ( triangle A B C, ) if ( angle A=72^{circ} ) and ( angle B=63^{circ} ) find the ( angle C ) |
7 |

339 | In the adjoining figure, ( A B=A C ) and ( A P perp B C . ) Then: ( mathbf{A} cdot A B=A P ) B. ( A BA P ) D. ( A B leq A P ) |
7 |

340 | Sum of internal angles of a triangle equals to ( mathbf{A} cdot 135^{circ} ) B. ( 180^{circ} ) c. ( 270^{circ} ) D. ( 360^{circ} ) |
7 |

341 | ( ln ) a ( Delta P R S, angle P R S=120^{circ} . A ) point ( Q ) is taken of ( P R ) such that ( P Q=Q S ) and ( Q R=R S ) then ( angle Q P S=dots ) A ( cdot 15^{circ} ) B. ( 30^{circ} ) ( c cdot 45^{circ} ) D. ( 12^{circ} ) |
7 |

342 | From the given triangle ( A B C, ) find the measure of an ( angle A C B ) |
7 |

343 | In ( Delta A B C, angle A=100^{circ}, angle B=30^{circ} ) and ( angle C=50^{circ}, ) then ( mathbf{A} cdot A B>A C ) B. ( A B=A C ) c. ( A B<A C ) D. None of these |
7 |

344 | Given: ( angle C A B=75^{circ} ) and ( angle C B A=50^{circ} ) Find the value of ( angle D A B+angle A B D ) |
7 |

345 | Find the value of ( y, ) if ( x=5^{circ} ) ( A cdot 50 ) 3.45 ( c cdot 32^{2} ) .38 ( ^{2} ) |
7 |

346 | In the figure, the value of ( x ) ( A cdot 40 ) B. 70 ( c cdot 110^{circ} ) D. 130 |
7 |

347 | If one angle of a triangle equals the sum of the other two angles, the triangle must be A. scalene B. right angled c. obtuse angled D. acute angled |
7 |

348 | A triangle can have: A. one right angle B. two right angles C . three obtuse angles D. none of these |
7 |

349 | In the figure below, ( angle Q>angle R ) and ( M ) is a point on ( Q R ) such that ( P M ) is the bisector of ( angle Q P R ) If the perpendicular from ( P ) on ( Q R ) meets ( Q R ) at ( N ) then prove that ( angle M P N=frac{1}{2}(angle Q-angle R) ) |
7 |

350 | n given fig. sides ( A B ) and ( A C ) of ( Delta A B C ) are produced to ( E ) and ( D ) respectively. If angle bisectors ( B O ) and ( C O ) of ( angle C B E ) and ( angle B C D ) meet each other at point ( O, ) then prove that: ( angle B O C=90^{circ}-frac{angle x}{2} ) |
7 |

351 | ( mathbf{n} ) Fig., ( mathrm{M}, mathrm{N} ) and ( mathrm{P} ) are the mid-points of ( A B, A C ) and ( B C ) respectively. If ( mathrm{MN}=3 mathrm{cm} ) ( mathrm{NP}=3.5 mathrm{cm} ) and ( mathrm{MP}=2.5 mathrm{cm}, ) calculate ( mathrm{BC}, mathrm{AB} ) and ( mathrm{AC} ) |
7 |

352 | The perimeter of an isosceles triangle is ( 42 mathrm{cm} ) and its base is ( 1 frac{1}{2} ) times its congruent sides. the area of the triangle | 7 |

353 | Construct an isosceles ( Delta A B C ) such that: (i) base ( A B=4.2 c m, ) base angle ( = ) ( 30^{circ} ) |
7 |

354 | The angles of triangle are in ratio 1: 3: 5 find the angles ( mathbf{A} cdot 20,60,100 ) в. 30,60,90 c. 45,60,75 D. 50,60,70 |
7 |

355 | ( ln triangle A B C ) the ( angle B=60^{circ}, angle C=45^{circ} ) Find ( angle A ) |
7 |

356 | Name the types of following triangles: ( triangle A B C ) with ( A B=8.7 mathrm{cm}, A C=7 mathrm{cm} ) and ( B C=6 c m ) |
7 |

357 | In fig ( 9.18, ) tangents PQ and PR are drawn to a circle such that ( angle R P Q=30^{0} . ) A chord RS is drawn parallel to the tangent PQ. Find the ( angle R Q S ) in degrees.Hint: Draw a line through ( Q ) and perpendicular to ( Q P ) |
7 |

358 | ( boldsymbol{P}(boldsymbol{3}, boldsymbol{4}) boldsymbol{Q}(boldsymbol{7},-boldsymbol{2}) ) and ( boldsymbol{R}(-boldsymbol{2},-1) ) are vertices of ( triangle P Q R ) write equation of median |
7 |

359 | ( operatorname{In} ) an acute triangle ( A B C, angle A B C= ) ( mathbf{4 5}^{circ}, boldsymbol{A B}=mathbf{3} ) and ( boldsymbol{A C}=sqrt{mathbf{6}} . ) The angle ( angle B A C, ) is A ( .60^{circ} ) B. 65 ( c cdot 75 ) D. ( 15^{circ} ) or ( 75^{circ} ) |
7 |

360 | If (0,0) and ( (3, sqrt{3}) ) are two vertices of an equilateral triangle then find third vertex. |
7 |

361 | If each angle of a triangle is less than the sum of the other two angles of it then the triangle is right-angled. State true or false A. True B. False |
7 |

362 | Find the approximate value of ( angle A ) in ( Delta A B C ) if ( 8 angle A=9 angle B=4 angle C ) A ( .40^{circ} ) B. ( 74^{circ} ) ( c cdot 86^{circ} ) D. ( 46.3^{circ} ) |
7 |

363 | In ( Delta A B C, ) D and ( E ) are two mid points of sides ( A B ) and ( A C ) respectively. If ( angle B A C=40^{circ} ) and ( angle A B C=65^{circ}, ) then ( angle C E D ) is A . 75 B. 125 ( c cdot 130 ) D. 105 |
7 |

364 | In an isosceles triangle the sine of the base angle is three times as large as the cosine of the vertex angle. Find the sine of the base angle. |
7 |

365 | In an isosceles triangle ( A B C, ) with ( A B=A C, ) the bisectors of ( angle B ) and ( angle C ) intersect each other ( O . ) Join ( A ) to ( O ) Show that: ( boldsymbol{O} boldsymbol{B}=boldsymbol{O} boldsymbol{C} ) |
7 |

366 | Prove that the median to the base of an isosceles triangle is perpendicular to the base. |
7 |

367 | If two sides of an isosceles ( Delta ) are ( 3 mathrm{cm} ) and ( 8 mathrm{cm}, ) then the length of the third side is : ( mathbf{A} cdot 3 mathrm{cm} ) B. ( 8 mathrm{cm} ) ( c .3 mathrm{cm} ) or ( 8 mathrm{cm} ) D. none |
7 |

368 | The points ( A(2 a, 4 a), B(2 a, 6 a) ) and ( C(2 a+sqrt{3} a, 5 a)(text { when } a>0) ) are vertices of A. an obtuse angled triangle B. an equilateral triangle c. an isosceles obtuse angled triangle D. a right angled triangle |
7 |

369 | Find the coordinates of the vertices of an equilateral triangle of side 2 a as shown in the figure. |
7 |

370 | Name the type of following triangle. Triangle with lengths of sides ( 7 mathrm{cm}, 8 mathrm{cm} ) and ( 9 mathrm{cm} ) |
7 |

371 | One angle of a triangle is ( 78^{circ} ) and the other two angles are in the ratio 7: 10 Calculate the bigger angle of the triangle. |
7 |

372 | n ( triangle A B C, ) the bisector ( A D ) of ( angle A ) is perpendicular to side ( B C . ) Show that ( A B=A C ) and ( triangle A B C ) is isosceles |
7 |

373 | PQR is a right-angled triangle with ( mathrm{QS} ) as the perpendicular to the hypotenuse. The ratio PS : SR is equal to A. ( mathrm{QP}: mathrm{QR} ) B ( cdot Q P^{2}: Q R^{2} ) ( c cdot 2: 3 ) D. None of the above |
7 |

374 | For a triangle ( A B C, ) the true statement is: A ( cdot A C^{2}=A B^{2}+B C^{2} ) B. ( A C=A B+B C ) c. ( A C>A B+B C ) D. ( A C<A B+B C ) |
7 |

375 | The cosine of the obtuse angle formed by medians drawn from the vertices of the acute angles of an isosceles rightangled triangle is ( -frac{k}{5}, ) where ( k= ) |
7 |

376 | n fig ( 6.41, ) if ( A B | D E, angle B A C=35^{circ} ) and ( angle C D E=53^{circ}, ) find ( angle D C E ) |
7 |

377 | In the adjoining figure, ( B O ) and ( C O ) are the bisectors of ( angle B ) and ( angle C ) of ( Delta A B C ) Show that ( angle B O C=90^{circ}+frac{1}{2} angle A ) |
7 |

378 | ( angle A D E ) | 7 |

379 | In the fig. Straight lines ( A B & C D ) pass through centre ( O . ) If angle ( angle D C E=40^{circ} ) ( & angle A O D=75^{circ} ) Find ( angle C D E & angle O B E ) |
7 |

380 | The angles of triangle are ( 45^{circ}, 60^{circ} ) find the third angle. | 7 |

381 | Find all possible lengths of the third side, if sides of a triangle have 3 and 9 ( mathbf{A} cdot 6<x<12 ) B . ( 5<x<12 ) c. ( 6<x<10 ) |
7 |

382 | In the following figure; ( A B ) is the largest side and ( B C ) is the smallest side of triangle ( A B C . ) Write the angles ( x^{0}, y^{0} ) and ( z^{0} ) in ascending order of their values. A ( cdot y^{0}<z^{0}<x^{0} ) В . ( z^{0}<y^{0}y^{0}>x^{0} ) D. ( z^{0}>x^{0}>y^{0} ) |
7 |

383 | The lengths of the sides of a triangle are proportional to the numbers 5,12 and ( 13 . ) The largest side of the triangle exceeds the smallest side by ( 1.6 mathrm{m} ) Find the perimeter and the area of the triangle. | 7 |

384 | In ( Delta P Q R, ) an exterior angle at ( R ) is represented by ( 5 x+10 . ) If the two non- adjacent interior angles are represented by ( 3 x+15 ) and ( 3 x-20 ) find the value of the exterior angle, ( angle R ) A ( .90^{circ} ) B. ( 80^{circ} ) ( c cdot 84^{circ} ) D. ( 85^{circ} ) |
7 |

385 | Prove that in an isosceles triangle, the median to the base is also perpendicular. |
7 |

386 | You have studied in Class IX, that a median of a triangle divides it into two triangles of equal areas. Verify this result for ( triangle A B C ) whose vertices are ( boldsymbol{A}(mathbf{4},-mathbf{6}), boldsymbol{B}(mathbf{3},-mathbf{2}) ) and ( boldsymbol{C}(mathbf{5}, mathbf{2}) ) |
7 |

387 | If two angles in a triangle are ( 75^{circ} ) and 95 then the third angle is ( _{–} ) A. 30 B. 20 ( c cdot 10^{circ} ) D. ( 40^{circ} ) |
7 |

388 | Prove that the sum of all interior angles of a ( Delta ) is ( 180^{circ} ) |
7 |

389 | In an isosceles triangle, one angle has the angle measure of ( 110^{circ} . ) Find sum of two other angles of the triangle. A ( .70^{circ} ) B . ( 30^{circ} ) ( mathbf{c} cdot 25^{circ} ) D. 26 |
7 |

390 | ( triangle A B C ) is an isosceles ( triangle ) with ( A B= ) ( A C ) side ( B A ) is produced to ( D ) such that ( A B=A D ) prove ( angle B C D ) is a right angle. |
7 |

391 | ( ln ) a ( Delta A B C, E ) and ( F ) are the mid-points of ( A C ) and ( A B ) respectively. The altitude AP to BC intersects FE at Q. Prove that ( boldsymbol{A} boldsymbol{Q}=boldsymbol{Q} boldsymbol{P} ) |
7 |

392 | Let’s write the measurement of the angles of triangle ( A B C ) if ( A B=B C ) and ( angle B A C+angle A C B=50^{circ} ) |
7 |

393 | What is the value of ( angle boldsymbol{R} ) ? A. 100 on В. ( 110^{circ} ) ( c cdot 120 ) 0.130 |
7 |

394 | n fig ( 10.49, ) ABCD is parallelogram CEperpAB,CFperpAD andangleBCE = 40^ Find the values of ( x, y ) and ( z ) |
7 |

395 | In the figure, given below, CE is the perpendicular to ( A B, angle A C E= ) ( 20^{circ} ) and ( angle A B D=50^{circ} . ) Find the measure of ( angle B D A ) A ( cdot 36^{circ} ) B. ( 60^{circ} ) ( c cdot 56^{circ} ) D. none of the above |
7 |

396 | ( ln a Delta A B C, ) if ( A B=A C ) and ( angle A=70^{circ} ) find ( angle B ) and ( angle C ) |
7 |

397 | In each of the following state if the statement is true (T) or false (F): An equilateral triangle is isosceles also. A. True B. False |
7 |

398 | In ( triangle A B C, angle B ) is a right angle. The median AD and BE are at right angles. Then angle ( C ) is A . 60 B. ( tan ^{-1}left(frac{1}{sqrt{2}}right) ) c. ( tan ^{-1} sqrt{2} ) D. 90 |
7 |

399 | State true or false: Sum of two sides of a triangle is greater than the third side. A. True B. False |
7 |

400 | The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is ( 10^{circ}, ) find the three angles. |
7 |

401 | In ( Delta A B C, angle B=30^{circ}, angle C=80^{circ} ) and ( angle A=70^{circ} ) then A ( . A B>B C<A C ) В. ( A B A C )c. ( A B>B C>A C ) D. ( A B<B C<A C ) |
7 |

402 | If ( triangle A B C ) is right angled at ( A ) and ( A D perp B C, ) then ( frac{B D}{D C}= ) ( ^{mathrm{A}} cdotleft(frac{A B}{A C}right)^{2} ) в. ( frac{A B}{A C} ) ( ^{mathrm{c}}left(frac{A B}{A D}right)^{2} ) D. ( frac{A B}{A D} ) |
7 |

403 | ( A D ) is an altitude of an isosceles triangle ( A B C ) in which ( A B=A C ) Show that, ( A D ) bisects ( B C ) |
7 |

404 | Which of the following triangle is a type of triangle, classified on the basis of its sides? A. Acute angle triangle B. Right angle triangle c. obtuse angle triangle D. Equilateral triangle |
7 |

405 | n the triangle ( A B C, angle A C E=130^{circ} ) ( operatorname{segment} A D=A D=D C, ) then find the measure of an ( angle A B C ) |
7 |

406 | ABC is a triangle and ( A D ) is median. If ( E ) is any point on ( A D, ) then ( mathbf{A} cdot A r(A B E)=A r(A C E) ) В. ( B E=C E ) c. ( A B+B E=A C+C E ) D. ( A E=frac{B E+C E}{2} ) |
7 |

407 | From a point within a triangle segments are drawn to the vertices A necessary and sufficient condition that the three triangles formed have equal areas is that the point be A. such that the three angles formed each have a measure of 120 B. the centre of the inscribed circle c. the centre of the circumscribed circle D. the intersection of the medians |
7 |

408 | The sum of the acute angles of an obtuse triangle is ( 70^{circ} ) and their difference is ( 10^{circ} . ) The largest angle is: A ( cdot 110^{circ} ) B. 105 ( c cdot 100^{circ} ) D. ( 95^{circ} ) |
7 |

409 | Calculate to find whether the given triangle is a right angled triangle. 4.10 B. Yes C. Insufficient data D. cannot calculate |
7 |

410 | Which of the following statements are true (T) and which are false (F)? Sum of any two sides of a triangle is greater than the third side. A . True B. False |
7 |

411 | ( A triangle A B C ) is right angled at ( A . L ) is a point on ( B C ) such that ( A L perp B C ) that ( angle B A L=angle A C B ) |
7 |

412 | Mark the correct alternative of the following. In figure, the value of ( x ) is? ( A cdot 84 ) B. 74 ( c .94 ) D. 57 |
7 |

413 | 70. In a triangle ABC, median is AD and centroid is O. AO = 10 cm. The length of OD (in cm) is (1) 6 (2) 4 (3) 5 (4) 3.3 |
7 |

414 | The angles of some triangles are given below. Classify each triangle acuteangled,obtuse-angled or right-angled on the basis of its angles. ( boldsymbol{a} cdot boldsymbol{9} boldsymbol{0}^{o}, boldsymbol{4} boldsymbol{5}^{o}, boldsymbol{4} boldsymbol{5}^{boldsymbol{o}} ) ( b .60^{circ}, 60^{circ}, 60^{circ} ) ( c .80^{circ}, 60^{circ}, 40^{circ} ) ( boldsymbol{d} . boldsymbol{9} boldsymbol{2}^{o}, mathbf{5} boldsymbol{0}^{o}, boldsymbol{3} boldsymbol{8}^{boldsymbol{o}} ) ( e .120^{circ}, 50^{circ}, 10^{circ} ) ( boldsymbol{f} cdot boldsymbol{9} boldsymbol{0}^{o}, boldsymbol{3} boldsymbol{5}^{o}, boldsymbol{5} boldsymbol{5}^{boldsymbol{o}} ) |
7 |

415 | n figure, show that ( 2(A C+B D)>A B+B C ) ( +mathrm{CD}+mathrm{DA} ) |
7 |

416 | State TRUE or FALSE In a triangle ( A B C, ) right-angled at ( B, B D ) is drawn perpendicular to AC. hence, ( mathrm{CDB}=angle mathrm{A} ) A. True B. False |
7 |

417 | ( boldsymbol{A}(mathbf{5}, mathbf{4}), boldsymbol{B}(-mathbf{3},-mathbf{2}) ) and ( boldsymbol{C}(mathbf{1},-mathbf{8}) ) are the vertices of a triangle ABC. Find the equation of median AD. |
7 |

418 | State whether the statement is true/false n a quadrilateral ( A B C D, A B+B C+C D+ ) ( mathrm{DA}<2(mathrm{BD}+mathrm{AC}) ) A. True B. False |
7 |

419 | In a triangle of base a, the ratio of the other sides is ( r(<1) . ) Show that the altitude of the triangle is less than or equal to ( frac{a r}{1-r^{2}} ) |
7 |

420 | ( ln Delta A B C, B C=A B ) and ( angle B=80^{circ} ) Then ( angle A ) is equal to A . ( 80^{circ} ) В . ( 40^{circ} ) ( c .50^{circ} ) D. ( 100^{circ} ) |
7 |

421 | Triangle ( A B C ) is angled at ( A . A D ) is drawn perpendicular to ( B C . ) If ( A B= ) ( 10 mathrm{cm}, A C=12 mathrm{cm}, ) find the area of ( triangle A B C . ) Also find the length of ( A D ) |
7 |

422 | In triangle ( A B C, angle A=angle B=52^{circ}, ) write the name of its largest side. ( A cdot A B ) B. BC ( c cdot c A ) D. None of these |
7 |

423 | In isosceles triangle ( boldsymbol{A B C}, boldsymbol{A B}=boldsymbol{A C} ) The side ( B A ) is produced to ( D ) such that ( boldsymbol{B A}=boldsymbol{A D} ) Hence, ( angle B C D=90^{circ} ) If the above statement is true then mention answer as 1 , else mention 0 if false |
7 |

424 | If sides of a triangle are ( 5,6, ) and ( 10, ) and the length of the median of biggest side id ( m, ) then find ( 100 m ) | 7 |

425 | n figure the sides ( A B ) and ( A C ) of ( Delta A B C ) are produced to point ( mathrm{E} ) and ( mathrm{D} ) repectively. If bisector BO and CO of ( angle C B E ) and ( angle B C D ) respectively meet a point ( 0, ) then ( angle B O C=90^{circ}-frac{1}{2} angle B A C ) |
7 |

426 | If two angles of a triangle are acute angles, then third angle A. is less than the sum of the two angles B. is an acute angle c. is the largest angle of the triangle D. may be an obtuse angle |
7 |

427 | fin ( Delta mathrm{ABC}, angle B=90^{circ}, angle C=45^{circ}, ) then find the angle ( A ) |
7 |

428 | In each of the following figure, find the value of ( x: ) |
7 |

429 | In the given figure, ( angle boldsymbol{X}= ) ( mathbf{6 2}^{circ}, angle boldsymbol{X} boldsymbol{Y} boldsymbol{Z}=mathbf{5 4}^{boldsymbol{o}} . ln triangle boldsymbol{X} boldsymbol{Y} boldsymbol{Z} ) If YO and ZO are the bisectors of ( angle X Y Z ) and ( angle X Z Y ) respectively find ( angle O Z Y ) and ( angle Y O Z ) |
7 |

430 | If in a ( triangle A B C, cos A=frac{sin B}{2 sin C}, ) then it is A. An isosceles triangles B. An equilateral triangle C . A right angled triangle D. None of these |
7 |

431 | In the figure, measure of ( angle x ) is ( mathbf{A} cdot 65^{circ} ) B ( .85^{circ} ) ( c cdot 75 ) D. 55 |
7 |

432 | Show that the sum of the three altitudes of a triangle is less than the sum of its three sides. |
7 |

433 | If ( D ) is any point on the side ( B C ) of ( Delta A B C ) such that ( Delta A D B ) and ( Delta A D C ) are equal in area, then A. AD is the median B. AD is the altitude c. AD is an angle bisector D. AD is any line |
7 |

434 | In the given figure, find ( angle M N R ) |
7 |

435 | n the given figure, the measure of ( angle B A C ) is A ( cdot 65^{circ} ) ( 3 cdot 50^{circ} ) ( c cdot 55^{circ} ) 0.60 |
7 |

436 | In the figure given ( Delta A B C ) is a right isosceles triangle with right angle at ( C ) CD is a parallel to ( A B ) and ( B D=B A ). The degree measure of ( angle D B C ) equals: A . ( 10^{circ} ) B . ( 15^{circ} ) ( c cdot 20^{circ} ) D. 25 |
7 |

437 | A right angled triangle has a base of ( 40 mathrm{cm}, ) height of ( 30 mathrm{cm} ) and hypotenuse of ( 50 mathrm{cm} . ) The triangle is rotated so that the hypotenuse forms the base. Find the altitude now. | 7 |

438 | In a square ( boldsymbol{P Q R S} ), an equilateral triangle ( triangle boldsymbol{T} boldsymbol{Q} boldsymbol{R} ) is formed, then ( boldsymbol{m} angle boldsymbol{P T S}-? ) A ( .75^{circ} ) В. ( 90^{circ} ) ( c cdot 120^{circ} ) D. ( 150^{circ} ) |
7 |

439 | The length of two sides of triangle are 6 ( mathrm{cm} ) and ( 10 mathrm{cm} . ) Between what two wholes numbers should lie the measure of the third sides? |
7 |

440 | ( ln ) a ( triangle A B C, A(-2,3), B(2,1) ) and ( C(1,2) . ) What is the foot of the altitude from the vertex ( A ) of the triangle ( A B C ? ) A ( .(1,4) ) в. (-1,3) c. (-2,4) D. (-1,4) |
7 |

441 | Differences of any two sides of a triangle is ( ldots ldots . . ) than the third side A. May be less or more B. More c. Equal D. Less |
7 |

442 | In figure (ii) given below, ( boldsymbol{A B} | boldsymbol{D} boldsymbol{E} ) and ( boldsymbol{B} boldsymbol{D} | boldsymbol{E} boldsymbol{F} . ) Prove that ( boldsymbol{D} boldsymbol{C}^{2}=boldsymbol{C} boldsymbol{F} times boldsymbol{A} boldsymbol{C} ) |
7 |

443 | The sum of angles of a triangle is equal to A ( .90^{circ} ) B . ( 120^{circ} ) ( c cdot 150^{circ} ) D. ( 180^{circ} ) |
7 |

444 | The angles of a triangle are ( (2 x+ ) ( left.30^{circ}right),left(3 x-110^{circ}right) ) and ( left(frac{5}{2} x+20^{circ}right), ) find the value of ( x ) A ( cdot 16^{circ} ) В. ( 32^{circ} ) ( c cdot 40^{circ} ) ( D cdot 50^{circ} ) |
7 |

445 | In the given triangle the value of ( x ) is A .55 B. ( 110^{circ} ) ( c cdot 60^{circ} ) D. ( 30^{circ} ) |
7 |

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