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

#### List of triangles Questions

Question No | Questions | Class |
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1 | In a right angled ( triangle mathrm{ABC}, mathrm{AC} perp ) the hypotenuse BC then ( A D^{2} ) is ( mathbf{A} cdot A C times C D ) B. ( A C times B A ) c. ( D C times B D ) D. None of these | 10 |

2 | In a squared sheet, draw two triangles of equal area such that the triangles are congruent.comment about perimeter. | 9 |

3 | Show that the diagonals of a rhombus divide it into four congruent triangles. | 9 |

4 | 66. In a quadrilateral ABCD, with un- equal sides if the diagonals AC and BD intersect at right angles, then (1) AB2 + BC2 = CD2 + DA2 (2) ABP + CD = BC2 + DA2 (3) AB2 + AD = BC + CD2 (4) AB2 + BC = 2(CD? + DA?) | 10 |

5 | In the adjoining figure ( triangle P Q R sim ) ( triangle boldsymbol{T} boldsymbol{S} boldsymbol{R} ) ldentify the corresponding vertices, corresponding sides and their ratios. | 10 |

6 | ABCD is a trapezium. Further if ( mathrm{CD}=4.5 ) ( mathrm{cm} ; ) find the length of ( 2 mathrm{AB} ) in ( mathrm{cm} ) | 10 |

7 | n given figure, ( angle C A B=90^{circ} ) and ( A D perp B C . ) If ( A C=75 mathrm{cm} . A B=1 mathrm{m} ) and ( B D=1.25 mathrm{m}, ) find ( A D ) | 10 |

8 | A ( 15 mathrm{m} ) long ladder reached a window 12 ( mathrm{m} ) high from the ground. On placing it against a wall at a distance ( x ) m. Find ( x ) | 10 |

9 | State true or false: In ( triangle A B C, A B=B C=C A=2 a ) and ( A D ) is perpendicular to side ( B C, ) then ( A D=2 a sqrt{3} ) A. True B. False | 10 |

10 | A vertical stick ( 12 mathrm{m} ) long casts a shadow ( 8 mathrm{m} ) long on the ground. At the same time a tower casts the shadow of length ( 40 mathrm{m} ) on the ground. Determine the height of the tower | 10 |

11 | f ( Delta A B C ) and ( Delta X Y Z ) are congruent then ( Delta A B C ldots ldots . Delta X Y Z ) ( A cdot cong ) B. ( = ) ( c cdot approx ) D. | 9 |

12 | State which pairs of triangles in Fig. are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form: | 10 |

13 | Determine by choosing the best option for the similarly of triangles theorem. ( D E | B C . ) Both ( triangle A D E & triangle A B C ) are similar by: A. SAS B. SSS ( c cdot A A A ) D. AAS | 10 |

14 | From a point ( Q, ) the length of the tangent to a circle is ( 24 mathrm{cm} ) and the distance of ( Q ) from the centre is ( 25 mathrm{cm} ) The radius of the circle is | 10 |

15 | ( A B=6.3 mathrm{cm}, mathrm{EC}=11.0 mathrm{cm}, mathrm{AD}=0.8 mathrm{cm} ) and ( A E=1.6 mathrm{cm} ) Enter 1 if true or 0 if false. | 10 |

16 | n fig. ( mathbf{7 . 8}, boldsymbol{O A}=boldsymbol{O B} ) and ( boldsymbol{O D}=boldsymbol{O C} ) Show that (i) ( Delta A O D cong Delta B O C ) and (ii) ( boldsymbol{A} boldsymbol{D} | boldsymbol{B} boldsymbol{C} ) | 9 |

17 | State and prove Basic proportionality (Thales) theorem. | 10 |

18 | In the figures, sides ( X Y ) and ( Y Z ) and median XA of a triangle XYZ are propotional to sidesDE,EF and median DB of ( triangle D E F ). Show that ( Delta X Y Z sim ) ( Delta D E F ) | 10 |

19 | In a triangle ( A B C, ) medians ( A D ) and ( B E ) are drawn. If ( mathrm{AD}=4, angle D A B=frac{pi}{6} ) and ( angle A B E=frac{pi}{3}, ) then the area of ( Delta A B C ) is A ( cdot frac{8}{3} ) в. ( frac{16}{3} ) c. ( frac{32}{3 sqrt{3}} ) D. ( frac{64}{3} ) | 10 |

20 | Two triangles are ……. if two sides and included angle of one triangle are equal to two sides and included angle of the other triangle. A. congruent B. unequal c. equilateral D. none of these | 9 |

21 | State whether the shapes in the given pair are similar. If they are similar enter else if not similar then enter 0 | 10 |

22 | Which of the following statements is true, if ( Delta P Q R cong Delta L M N ? ) ( mathbf{A} cdot P Q=M N ) в. ( Q R=L N ) c. ( P R=L M ) D. ( Q P=M L ) | 9 |

23 | n Fig., ( A B C ) and ( A M P ) are two right triangles, right angled at ( B ) and ( M ) respectively. Prove that: ( triangle A B C sim triangle A M P ) | 10 |

24 | Which one of the four trapezoids is not similar to the other three? ( A cdot A ) B. B ( c cdot c ) ( D ) | 10 |

25 | n given figure, express ( x ) in terms of ( a, b ) and ( c ) | 10 |

26 | The areas of two similar triangles are ( 100 mathrm{cm}^{2} ) and ( 64 mathrm{cm}^{2} ). If the median of greater side of first triangle is ( 13 mathrm{cm} ) find the corresponding median of the other triangle. A . ( 20 mathrm{cm} ) B. ( 15 mathrm{cm} ) c. ( 10 mathrm{cm} ) D. ( 16 mathrm{cm} ) | 10 |

27 | 61. If G is the centroid of A ABC and A ABC = 48 cm², then the area of A BGC is (1) 32 cm (2) 8 cm (3) 16 cm2 (4) 24 cm | 9 |

28 | If ( Delta mathbf{A B C} sim ) ( Delta P Q R ) then find value of ( y+3 ) | 10 |

29 | In the given figure AE is bisector of ( angle B A C ) and of ( angle B D C . ) show that ( Delta A B D cong A C D ) and hence ( B D=C D ) | 10 |

30 | n given figures the two triangles are ( operatorname{similar} Delta A B C sim Delta D E F ) if ( E D=7 ) find the length of ( boldsymbol{A C} ) ( A ) B. 14 ( c ) ( D cdot 2 ) | 10 |

31 | In two similar triangles ( A B C ) and ( P Q R ), if their corresponding altitudes ( A D ) and ( P s ) are in the ratio ( 4: 9, ) find the ratio of the areas of ( triangle A B C ) and ( triangle P Q R ) A . 16: 81 B. 9: 16 c. 81: 16 D. 16: 9 | 10 |

32 | Which among the following is/are not correct? This question has multiple correct options A. The ratios of the areas of two similar triangles is equal to the ratio of their corresponding sides. B. The areas of two similar triangles are in the ratio of the corresponding altitudes. C. The ratio of area of two similar triangles are in the ratio of the corresponding medians. D. If the areas of two similar triangles are equal, then the triangles are congruent | 10 |

33 | Triangle ( A B C ) is similar to triangle PQR. Find ( P Q ) | 10 |

34 | ratio ( boldsymbol{O P}: boldsymbol{O} boldsymbol{D}=boldsymbol{m}: boldsymbol{n} . ) Find ( boldsymbol{m}+boldsymbol{n} ) | 10 |

35 | If diagonal of a rectangle is ( 26 mathrm{cm} ) and one side is ( 24 mathrm{cm} ).Find the other side? | 10 |

36 | If ( Delta A B C cong Delta F E D ) under the correspondence ( boldsymbol{A B C} leftrightarrow boldsymbol{F E D}, ) write all the corresponding congruent parts of the triangles. | 9 |

37 | In the figure given below, ( angle boldsymbol{P}=angle boldsymbol{R} boldsymbol{T} boldsymbol{S} ) Prove that ( triangle R P Q sin triangle R T S ) | 10 |

38 | In ( triangle A B C, angle C=90^{circ} . ) If ( B C=a, A C= ) ( b ) and ( A B=c, ) find ( c ) when ( a=8 c m ) and ( b=6 mathrm{cm} ) ( mathbf{A} cdot 10 mathrm{cm} ) в. ( 14 mathrm{cm} ) c. ( 15 mathrm{cm} ) D. ( 20 mathrm{cm} ) | 10 |

39 | adod ( operatorname{In} Delta A B C, angle A=90^{circ} ) and ( A D perp B C ) Then, ( Delta A B C sim Delta D A C ) A. True B. False | 10 |

40 | Two equilateral triangles with side ( 4 mathrm{cm} ) and ( 6 mathrm{cm} ) are ( _{–}-_{-} ) triangles. A. similar B. congruent c. both D. none of these | 10 |

41 | Which line is parallel to ( B C ? ) A ( . P Q ) 3.57 ( c, O R ) D ( S ) h | 10 |

42 | n the figure given below, ( Delta B C A cong ) ( Delta B C D . ) Corresponding angle to ( angle D ) is ( A cdot angle B ) B. ( angle C ) ( c . angle D ) 0.4 | 9 |

43 | State true or false: In quadrilateral ( A B C D, ) its diagonals ( A C ) and ( B D ) intersect at point ( O, ) such that ( frac{boldsymbol{O C}}{boldsymbol{O A}}=frac{boldsymbol{O D}}{boldsymbol{O B}}=frac{1}{3}, ) then ( triangle boldsymbol{O} boldsymbol{A} boldsymbol{B} sim triangle boldsymbol{O C D} ) A. True B. False | 10 |

44 | 62. If the circumcentre of a triangle lies on one of the sides then the orthocentre of the triangle lies on (1) one of the vertices (2) on the same side of the trian- gle (3) outside the triangle (4) strictly inside the triangle | 9 |

45 | The two triangles below are similar ( Delta A B C sim Delta E F D ) What is the value of ( angle B ? ) A . ( 80^{circ} ) B. 30 ( c cdot 70^{circ} ) D. 60 | 9 |

46 | I a ( triangle A B C, angle A=90^{circ}, C A=A B ) and ( D ) is a point on AB produced prove that ( boldsymbol{D} boldsymbol{C}^{2}=boldsymbol{B} boldsymbol{D}^{2}=boldsymbol{2} boldsymbol{A} boldsymbol{B} times boldsymbol{A} boldsymbol{D} ) | 10 |

47 | Find the zeros of the quadratic polynomial ( x^{2}+7 x+12, ) and verify the relation between the zeros and its coefficients. | 10 |

48 | Let ( A B C ) be an equilateral triangle and suppose KLMN be a rectangle with ( boldsymbol{K}, boldsymbol{L} ) on ( mathrm{BC}, mathrm{M} ) on ( mathrm{AC} ) and ( mathrm{N} ) on AB. If ( frac{A N}{N B}=2 ) and area of triangle BKN is ( 6, ) then area of triangle ( A B C ) is equal to A . 48 B. 54 c. 96 D. 108 | 9 |

49 | In the following figure, ( X Y ) is parallel to ( B C, A X=9 c m, X B=4.5 mathrm{cm} ) and ( B C=18 mathrm{cm} . ) Find the value of ( x y ) ( A cdot 14 ) 3. 12 ( c .16 ) D. 18 | 10 |

50 | Side ( A B ) and ( B C ) and median ( A D ) of a triangle ( A B C ) are respectively proportional to sides ( P Q ) and ( Q R ) and median ( P M ) of ( P Q R ) Show that ( A B C sim P Q R ) | 10 |

51 | The ratio of the corresponding sides of the two similar triangles is 2: 3 and the area of the smaller triangle is 64 sq.cm. Find the area of larger triangle. | 10 |

52 | Find ( A B ) ( mathbf{A} ) 3 ( c ) ( D ) | 10 |

53 | Find the value of ( frac{K N}{L M} ) from the given figure. A в. ( frac{2}{5} ) c. ( frac{2}{3} ) D. 5 ( overline{3} ) | 10 |

54 | (i) If area ( (triangle A B C)=16 mathrm{cm}^{2}, ) area ( (triangle ) ( mathrm{DEF}=25 mathrm{cm}^{2} ) and ( mathrm{BC}=2.3 mathrm{cm}, ) find EF. (ii) If area ( (triangle A B C)=9 c m^{2}, operatorname{area}(triangle D E F) ) ( =64 mathrm{cm}^{2} ) and ( mathrm{DE}=5.1 mathrm{cm}, ) find ( mathrm{AB} ) (iii) If ( A C=19 mathrm{cm} ) and ( mathrm{DF}=8 mathrm{cm}, ) ratio of the area of two triangles. (iv) If area ( (triangle A B C)=36 mathrm{cm}^{2}, ) area ( (triangle ) DEF) ( =64 mathrm{cm}^{2} ) and ( mathrm{DE}=6.2 mathrm{cm}, ) find ( mathrm{AB} ) (v) If ( A B=1.2 mathrm{cm} ) and ( mathrm{DE}=1.4 ) find the ratio of the areas of triangle ( A B C ) and DEF. | 10 |

55 | In the given figure, the line segment ( X Y ) is parallel in ( A C ) of ( Delta A B C ) and is divided the triangle into two parts of equal areas then ( frac{A X}{A B}=frac{sqrt{2}-1}{sqrt{2}} ) A . True B. False | 10 |

56 | 58. The angles of two right angled triangles (AABC and APQR) are 45° and 60° respectively and ZB and 29 are right angles and AB = 5 cm, then PQ will be equal to (1) 7.5 cm (2) 5.0 cm (3) 6.7 cm (4) None of these | 9 |

57 | In the figure, ( C D ) and ( R S ) are respectively the medians of ( triangle A B C ) and ( triangle P Q R ) If ( triangle A B C sim triangle P Q R, ) prove that (i) ( triangle A D C sim triangle P S R ) (ii) ( frac{C D}{R S}=frac{A B}{P Q} ) | 10 |

58 | In a triangle ( P Q R, L ) and ( M ) are two points on the base ( Q R, ) such that ( angle L P Q= ) ( angle Q R P ) and ( angle R P M=angle R Q P . ) Prove that ( boldsymbol{P Q}^{2}=boldsymbol{Q} boldsymbol{R} times boldsymbol{Q} boldsymbol{L} ) | 10 |

59 | ( A B=x c m, B C=(4 x+4) mathrm{cm} ) and ( A C=(4 x) ) +5) ( mathrm{cm} . ) Find ( mathrm{AC} ) | 10 |

60 | In the figure given below, if DE ( | mathrm{BC} ) then the value of ( x ) equals to: ( A cdot 3 mathrm{cm} ) B. ( 2 mathrm{cm} ) ( c cdot 4 mathrm{cm} ) D. ( 6.7 mathrm{cm} ) | 10 |

61 | Two plane figures are said to be congruent if they have A. The same size B. The same shape c. The same size and the same shape D. none | 9 |

62 | Triangles ( A B C ) and DEF are similar. If their areas are ( 64 mathrm{cm}^{2} ) and ( 49 mathrm{cm}^{2} ) and if ( A B ) is ( 7 mathrm{cm}, ) then find the value of DE. ( A cdot 8 mathrm{cm} ) в. ( frac{49}{8} mathrm{cm} ) c. ( frac{8}{49} mathrm{cm} ) D. ( frac{64}{7} mathrm{cm} ) | 10 |

63 | In the figure, ( triangle A B C ) is right angled at ( B . D ) is any point on ( A B ) ( operatorname{seg} D E perp operatorname{sid} e A C . ) If ( A D= ) ( 6 mathrm{cm}, A B=12 mathrm{cm} A C=18 mathrm{cm} . ) Find ( A E ) ( A cdot 5 c m ) в. 3 ст ( c .4 c m ) ( 0.6 mathrm{cm} ) | 10 |

64 | Which of the following statements is incorrect when ( Delta P Q R cong Delta L M N ? ) ( mathbf{A} cdot angle P=angle L ) в. ( angle Q=angle M ) c. ( angle R=angle N ) D. none of these | 9 |

65 | Give any two real-life examples of congruent shapes. | 9 |

66 | Draw a ( triangle A B C ) in which ( B C= ) ( mathbf{6} c boldsymbol{m}, boldsymbol{A} boldsymbol{B}=mathbf{4} boldsymbol{c m} ) and ( boldsymbol{A} boldsymbol{C}=mathbf{5} boldsymbol{c m} ) Draw a triangle similar to ( triangle A B C ) with its sides equal to ( left(frac{3}{4}right)^{t h} ) of the corresponding sides of ( triangle boldsymbol{A B C} ) | 10 |

67 | Fill in the blanks. The perimeters of two similar triangles are ( 25 mathrm{cm} ) and ( 15 mathrm{cm} ) respectively. If one side of the first triangle is ( 9 mathrm{cm}, ) then corresponding side of second triangle is | 10 |

68 | The corresponding altitudes of two similar triangles are ( 6 mathrm{cm} ) and ( 9 mathrm{cm} ) respectively. Find the ratio of their areas. | 10 |

69 | Instead of walking along two adjacent sides of a rectangular field,a boy book a short – cut along the diagonal of the field and saved a distance equal to ( 1 / 2 ) the longer side. The ratio of the shorter side of the rectangle to the longer side was: ( A ) B. ( c cdot frac{1}{4} ) 0.3 ( E ) | 10 |

70 | ( triangle A B C sim triangle D E F ) and their perimeters are ( 32 mathrm{cm} ) and ( 24 mathrm{cm} ) respectively. If ( A B=10 mathrm{cm}, ) Find ( D E ) | 10 |

71 | fin a ( triangle D E F, G H | E F ) and ( D G ) ( boldsymbol{E G}=boldsymbol{2}: boldsymbol{3} ) then the value of ( frac{operatorname{ar}(triangle D G H)}{operatorname{ar}(triangle D E F)} ) A ( cdot frac{2}{15} ) B. ( frac{4}{15} ) c. ( frac{4}{25} ) D. ( frac{2}{25} ) | 10 |

72 | 61. In a triangle ABC, ZA = 90°, 2C = 55°, AD IBC. What is the value of ZBAD? (1) 35° (2) 60° (3) 45° (4) 55° | 9 |

73 | Two triangles ( A B C ) and ( P Q R ) are ( operatorname{similar}, ) if ( B C: C A: A B=1: 2: 3 ) then ( frac{Q R}{P R} ) A ( cdot frac{3}{2} ) B. ( frac{1}{2} ) c. ( frac{1}{sqrt{2}} ) D. ( frac{2}{3} ) | 10 |

74 | n ( triangle boldsymbol{R} boldsymbol{S T} ), line ( boldsymbol{P Q} | ) segST ( , boldsymbol{R}-boldsymbol{P}-boldsymbol{S} ) and ( boldsymbol{R}-boldsymbol{Q}-boldsymbol{T} . ) If ( boldsymbol{R} boldsymbol{P}=boldsymbol{4}, boldsymbol{P} boldsymbol{S}= ) ( 8, R Q=3, ) then find ( Q T ) | 10 |

75 | Is similarity of triangles different from similarity of polygons? | 10 |

76 | ( O^{prime} ) is a point inside of ( triangle A B C . ) The bisector of ( angle A O B, angle B O C, angle C O A ) meet the sides ( A B, B C ) and ( C A ) in points ( D, E ) and ( F ) respectively, then ( boldsymbol{A} boldsymbol{D} cdot boldsymbol{B} boldsymbol{E} cdot boldsymbol{C} boldsymbol{F}= ) A. ( D B . E C . F A ) в. ( A D . E C . F A ) c. ( D B . B ) E.FA D. DB.BE.CF | 10 |

77 | In the given figure, ( triangle A B C ) is an isosceles right angled triangle with ( angle B=90 ) such that ( P Q perp A C, S T perp A C ) where Plies on AB and S lies on BC. Then prove that ( triangle A Q P sim triangle C T S ) | 10 |

78 | 59. The ratio of the areas of the incircle and the circumcircle of a square is : (1) 1:2 (2) 2:3 (3) 3:4 (4) 4:5 | 10 |

79 | n the given figure, ( P S=P R . angle T P S= ) ( angle Q P R ) Then ( P T=P Q ) 4 True 3. Fals | 10 |

80 | The corresponding sides of two similar triangles are ( 4 mathrm{cm} ) and ( 5 mathrm{cm} ) respectively, find the ratio of the area of the first triangle to the area of the 2 nd triangle: | 10 |

81 | There were three circular tracks made in a park having the same middle point but their radii was different. These tracks will be called A. Not similar B. Similar c. congruent D. All of the above | 10 |

82 | Check whether the following pairs of triangles are congruent. If they are congent, state the congruence criterion. | 9 |

83 | In the given figure, ( triangle A B C ) is right angled at ( B ). If ( B D perp A C ), which of the following is/are true? A. ( triangle A B C sim triangle A D B ) B. ( triangle A B C sim triangle B D C ) c. ( triangle A D B sim triangle B D C ) D. ( triangle A B C sim triangle D B C ) | 10 |

84 | Let ( triangle A B C sim triangle D E F ) and their areas be ( 64 mathrm{cm}^{2} ) and ( 121 mathrm{cm}^{2} ) respectively. If ( boldsymbol{E F}=mathbf{1 5 . 4} boldsymbol{c m}, ) find ( boldsymbol{B C} ) | 10 |

85 | Triangles ( A B C ) and ( P Q R ) are similar Find the angle ( B ) ( A cdot 30^{circ} ) B. ( 60^{circ} ) ( c cdot 90^{circ} ) 0.70 | 10 |

86 | If the vertices of an equilateral triangle have integral co-ordinates, then A. Such a triangle is not possible B. The area of the triangle is irrational C. The area of the triangle is an integer D. The area of the triangle is rational but not an integer | 9 |

87 | Two quadrilaterals, a square and a rectangle are not similar as they ( ldots ). in shape as well as size. A . Differ B. Are same c. Do not siffer D. Angles also differ | 10 |

88 | ( triangle A B C ) is similar to ( triangle X Y Z ) by ( S A S ) similarity. If in ( triangle A B C A B= ) ( mathbf{1 2}, boldsymbol{B C}=mathbf{8}, angle boldsymbol{B}=mathbf{6 0} ) and in ( triangle boldsymbol{X} boldsymbol{Y} boldsymbol{Z} boldsymbol{X} boldsymbol{Y}=mathbf{3}, angle boldsymbol{Y}=mathbf{6 0} . ) Find the value of ( Y Z ) A . 15 B . 20 ( c cdot 4 ) D. 2 | 10 |

89 | 60. The number of points in the plane of a triangle which are equidis- tant from the sides of the trian- gle is (1) 1 (2) 2 (3) 3 (4) 4 | 9 |

90 | In the figure, find the area of ( triangle boldsymbol{P Q R} ) and the height ( P S ). | 10 |

91 | In figure ( angle mathbf{1}=angle mathbf{2} ) and ( triangle boldsymbol{N} boldsymbol{S} boldsymbol{Q} cong ) ( triangle M T R, ) then prove that ( triangle P T S sim ) ( triangle boldsymbol{P R Q} ) | 10 |

92 | Without drawing exact triangles, state, giving reasons, whether the given pairs of triangle are congruent or not: In ( Delta A B C ) and ( Delta P B C ; A B= ) ( boldsymbol{B P}, boldsymbol{A C}=boldsymbol{P C} ) | 10 |

93 | n ( triangle A B C, angle A B C=90^{circ}, B D perp A C ) If ( boldsymbol{B} boldsymbol{D}=boldsymbol{8} mathbf{c m}, boldsymbol{A} boldsymbol{D}=boldsymbol{4} mathrm{cm}, ) find ( boldsymbol{C} boldsymbol{D} ) | 10 |

94 | Find the length of ( B D ) in the given figure ( mathbf{A} ) B. ( c cdot 12 ) 0.15 | 10 |

95 | The altitude of an equilateral triangle of side lenght of ( 2 sqrt{3} mathrm{cm} ) is: A ( cdot frac{sqrt{3}}{2} c ) в. ( frac{1}{2} c m ) c. ( frac{sqrt{3}}{4} c ) D. 3 ст | 10 |

96 | ( A B C ) is a triangle whose altitudes ( B E ) and ( C F ) to sides ( A C ) and ( A B ) respectively, are equal. Which of these conditions is not required to prove ( triangle A B E cong triangle A C F ? ) A ( . angle B=angle C ) B. ( angle B A E=angle F A C ) c. ( angle A F C=angle A E B ) D. ( B E=C F ) | 9 |

97 | In triangle ( A B C ), the altitude from ( A ) to ( B C ) meets ( B C ) at ( D ) and the altitude from ( B ) to ( C A ) meets ( A D ) at ( H . ) If ( A D= ) ( 4 mathrm{cm}, B D=3 mathrm{cm} ) and ( C D=2 mathrm{cm} ) and if ( frac{A B}{B D}=frac{A H}{H D}, ) then the length of ( H D ) is ( ^{text {A } cdot frac{sqrt{5}}{2} mathrm{cm}} ) в. ( frac{3}{2} mathrm{cm} ) c. ( sqrt{5} mathrm{cm} ) D. cn | 10 |

98 | PQR is a triangle. S is a point on the side QR of ( Delta ) PQR such that ( angle mathrm{PSR}=angle mathrm{QPR} / ) Given ( boldsymbol{Q} boldsymbol{P}=mathbf{8 c m}, P mathrm{R}=mathbf{6 c m} ) and ( mathbf{S R}=mathbf{3} ) ( mathrm{cm} ) (I) Prove ( Delta mathrm{PQR} sim Delta ) SPR (II) Find the length of QR and PS areaof ( Delta P Q R ) (III) ( frac{d r e a o f Delta S P R}{a r e a o f} ) | 10 |

99 | 87. The ratio of the areas of two isos- celes triangles having the same vertical angle (i.e. angle between equal sides) is 1:4. The ratio of their heights is (1) 1:4 (2) 2:5 (3) 1:2 (4) 3:4 | 10 |

100 | n figure ( D ) and ( E ) are the mid points of sides ( A B ) and ( A C ) respectively of ( triangle A B C ) Find ( angle E D B ) ( A cdot 110 ) ( 3 cdot 120 ) ( c cdot 70^{circ} ) ( D cdot 80 ) | 10 |

101 | Prove that if the areas of two similar triangle are equal, then the triangles are congruent | 9 |

102 | Fill in the blank: ( angle C cong ) ( A cdot Z ) 3. ( angle Q ) ( c . angle R ) D. ( angle A ) | 10 |

103 | 66. AABC and ADBC are two isosce- les triangles formed on opposite side at the same base BC and Z A= 80º and ZD = 70° then ZABD will be equal to (1) 115° (2) 150° (3) 75° (4) 105° | 9 |

104 | The areas of two similar triangles are ( 121 mathrm{cm}^{2} ) and ( 81 mathrm{cm}^{2} ) respectively. Find the ratio of their corresponding heights. A ( cdot frac{11}{9} ) в. ( frac{10}{9} ) ( c cdot frac{9}{11} ) D. ( frac{9}{10} ) | 10 |

105 | n the figure, ( angle P Q S=angle P R T ) and ( mathrm{QS}=mathrm{TR} . ) then ( Delta P Q S cong Delta P R T mathrm{by} ) congruence postulate ( A cdot operatorname{sas} ) B. sss ( c . ) RHS D. AAS | 9 |

106 | n the figure of ( Delta A B C, D E | A B ) ( f A D=2 x, D C=x+3, B E=2 x-1 ) and ( C E=x, ) then find the value of ( x ) | 10 |

107 | In ( triangle A B C, angle A B C=90^{circ} ) and BM is the altitude. If ( A M=16 ) MC Prove that ( A B= ) ( 4 mathrm{BC} ) | 10 |

108 | In the adjoining figure ( D E | B C ), if ( A C=18 c m, A D=6 c m, A B=12 c m ) find ( boldsymbol{E C} ) ? | 10 |

109 | ff ( Delta D E F equiv Delta B C A, ) write the part(s) of ( Delta B C A ) that correspond to ( angle F ) | 9 |

110 | ( f(-A) ) and ( C B ) are congruent, ( A C=12 ) then find ( B C ). 4. 12 3.10 ( c ) 2.2 | 10 |

111 | From the following data, state if ( triangle A B C sim triangle D E F ) or not ( angle B=65^{circ}, angle C=82^{circ}, angle D=33^{circ}, angle F= ) ( mathbf{6 5}^{circ} ) | 10 |

112 | Assertion: Two ( Delta ) s are said to be congruent if two sides and an angle of the one triangle are respectively equal to the two sides and an angle of the other triangle. Reason: Two ( Delta ) s are congruent if two sides and the included angle of the one Two statements A and R are given above. Which of the following statements is correct? | 9 |

113 | n Fig. ( D ) is a point on hypotenuse ( A C ) of ( triangle A B C, ) such that ( B D perp A C, D M perp B C ) and ( D N perp A B ) Prove that: (i) ( D M^{2}=D N cdot M C ) (ii) ( D N^{2}=D M cdot A N ) | 10 |

114 | n given figure ( A B C D ) is a trapezium in which ( A B | C D ) and ( A D=B C . ) Show that (i) ( angle boldsymbol{A}=angle boldsymbol{B} ) (ii) ( angle C=angle D ) (iii) ( triangle A B C cong triangle B A D ) (iv) diagonal ( A C=operatorname{diagonal~} B D ) | 9 |

115 | If ( D E | B C ) in ( triangle A B C, A D= ) ( 1.5 mathrm{cm}, B D=3 mathrm{cm} ) and ( A E=1 mathrm{cm}, ) then find ( E C(text { in } mathrm{cm}) . ) | 10 |

116 | n the above figure find the ratio between the ( triangle A O B ) and ( triangle C O D, ) if ( A B= ) ( mathbf{3} C D ) | 10 |

117 | Prove that “In a trapezium, the line joining the mid points of non-parallel sides is (i) parallel to the parallel sides and (ii) Half of the sum of the parallel sides” | 10 |

118 | Find the similarity statement A. ( Delta T S R sim Delta P Q R ) B. ( Delta T P S sim Delta Q R T ) c. ( Delta R P Q sim Delta T R P ) D. ( Delta S R Q sim Delta P Q S ) | 10 |

119 | 71. Two medians AD and BE of AABC intersect at G at right angles. If AD = 9 cm and BE = 6 cm, then the length of BD, in cm, is (1) 10 (2) 6 (3) 5 (4) 3 | 9 |

120 | ( Delta A P B ) is similar to ( Delta C P D ) State whether the above statement is true or false. | 10 |

121 | n which of the following cases the pairs of triangles are similar? Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form | 10 |

122 | State True or False. If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in the same ratio (proportional), then the triangles are similar. A. True B. False | 10 |

123 | In the following figure, ( M ) is midpoint of BC of a parallelogram ABCD. DM intersects the diagonal ( A C ) at ( P ) and AB produced at E. Then ( mathbf{A} cdot P E=3 P D ) B. ( P E=2 P D ) c. ( P E=P D ) ( D . P E=4 P D ) | 10 |

124 | 70. ABC is an equilateral triangle and O is its circumcentre, then the ZAOC is (1) 100° (2) 110° (3) 120° (4) 130° | 9 |

125 | If the areas of two similar triangles are equal then the triangles: A. are congruent B. have equal length of corresponding sides c. (A) and (B) D. None of these | 10 |

126 | 65. Two chords AB and CD of a cir- cle intersect at P inside the cir- cle and PA = 8 cm, AB = 14 cm, PC = 4, cm then find the length of CD (1) 6 cm (2) 10 cm (3) 12 cm (4) 16 cm | 10 |

127 | 68. If a, b and care the sides of a triangle and a + b + c = ab + bc + ca, then the triangle is (1) right-angled (2) obtuse-angled (3) equilateral (4) isosceles | 10 |

128 | ( ln Delta A B C, ) a line is drawn parallel to ( B C ) to meet sides ( A B ) and ( A C ) in ( D ) and ( E ) respectively. If the area of the ( Delta A D E ) is ( frac{1}{9} ) times area of the ( Delta A B C, ) then the value of ( frac{A D}{A B} ) is equal to: A ( cdot frac{1}{3} ) B. ( c cdot frac{1}{5} ) D. | 10 |

129 | n the given figure, the value of ( x text { (in } c m) ) is : 4 B. ( c ) ( D ) | 10 |

130 | Find the unknown length ( x ) in the following figures:- | 10 |

131 | ( angle A D C=angle B C D ) | 9 |

132 | If the ratio of the perimeter of two similar triangles is ( 4: 25, ) then find the ratio of the areas of the similar triangles | 10 |

133 | Two sides of a triangle are ( 64 mathrm{m} ) and 48 m. If height of the triangle corresponding to ( 48 mathrm{m} ) side is ( 6 mathrm{m} ), then the height of the triangle corresponding to ( 64 mathrm{m} ) side is ( 4.5 mathrm{m} ) If true then enter 1 and if false then enter 0 | 10 |

134 | If all the three altitudes of a triangle are equal, the triangle is equilateral. State whether the above statement is true or false. A. True B. False | 10 |

135 | The perimeter of two similar triangle are ( 30 mathrm{cm} ) and ( 20 mathrm{cm} . ) If one side of first triangle is ( 12 mathrm{cm} ) determine the corresponding side of second triangle. A. ( 8 mathrm{cm} ) в. ( 4 mathrm{cm} ) ( mathrm{c} .3 mathrm{cm} ) D. ( 16 mathrm{cm} ) | 10 |

136 | If ( A B C ) and ( B D E ) are two equilateral triangles such that ( D ) is the mid-point then find ( a r(triangle A B C): a r(triangle B D E) ) | 10 |

137 | 61. Let a, B. y be the three angles of a triangle ABC such that a +B< 7. Then A ABC is (1) Right angled (2) Acute angled (3) Obtuse angled (4) Isosceles | 9 |

138 | 67. The an The area of the incircle of an equi- lateral triangle of side 42 cm is (Take n = 27 (1) 231 cm2 (2) 462cm2 (3) 22/3 cm2 (4) 924 cm2 | 10 |

139 | Identify the postulate, based on which the given pair of triangle can be said similar? A. SAS similarity postulate B. AAA similarity postulate c. sss similarity postulate D. AAS similarity postulate | 10 |

140 | In a squared sheet, draw two triangles of equal area such that the triangles are not congruent. What can you say about their perimeters? | 9 |

141 | Give any two real-life examples for congruent shapes. | 9 |

142 | If corresponding angles of two triangles are equal, then they are known as A . Equiangular triangles B. Adjacent angles c. supplementary angles D. complementary angles | 10 |

143 | Which of the following is true? A. The ratio of sides of two similar triangles is same as the ratio of their corresponding altitudes. B. The ratio of sides of two similar triangles is same as the ratio of their corresponding perimeters. C. The ratio of sides of two similar triangles is same as the ratio of their corresponding area D. The ratio of sides of two similar triangles is same as the ratio of their corresponding medians. | 10 |

144 | n fig, If ( Delta A B E cong Delta A C D, ) show that ( Delta A D E ) is similar to ( Delta A B C ) | 10 |

145 | 56. In a AABC, AB? + AC = BC? and BC = V2 AB, then ZABC is : (1) 30° (2) 45° (3) 60° (4) 90° | 10 |

146 | If ( Delta A B C equiv Delta F E D ) under the correspondence ( A B C leftrightarrow F E D, ) write all the corresponding congruent parts of the triangles. | 9 |

147 | Triangle ( A ) has a base of ( x ) and a height of ( 2 x . ) Triangle ( B ) is similar to triangle ( A ) and has a base of ( 2 x ). What is the ratio of the area of triangle ( A ) to triangle ( B ? ) A . 1: 2 B. 2: ( c cdot 2: 3 ) D. 1: 4 | 10 |

148 | Which one of the four hexagons is not similar to the other three? ( A ) B. B ( c cdot c ) D. | 10 |

149 | Given line ( A B ) is parallel to line ( C D ) ( angle A G E ) and ( angle B G H ) are: A. Non-congruent B. congruent c. Supplementary D. None of these | 9 |

150 | State whether the following triangles are congruent or not? Give reasons for your answer | 9 |

151 | In ( triangle boldsymbol{L} M boldsymbol{N}, triangle boldsymbol{L}=boldsymbol{6} boldsymbol{0}^{circ}, angle boldsymbol{M}=mathbf{5 0}^{circ} ) If ( angle L M N sim triangle P Q R ) then the value of ( angle R ) is A ( .40^{circ} ) B . ( 60^{circ} ) ( c cdot 70^{circ} ) D. ( 110^{circ} ) | 10 |

152 | n Fig. ( boldsymbol{A D} perp boldsymbol{C D} ) and ( boldsymbol{C B} perp boldsymbol{C D .} ) If ( A Q=B P ) and ( D P=C Q, ) prove that ( angle D A Q=angle C B P ) | 9 |

153 | ( ln Delta P Q R, ) if ( P R^{2}=P Q^{2}+Q R^{2}, ) prove that ( angle Q ) is right angle. | 10 |

154 | 70. AABC is an isosceles triangle where LB = 90°. If similar tri- angles AABE and AACD are formed on AB and AC then the ratio of the areas of AABE and AACD will be (1) 1:2 (2) 1:3 (3) 2:3 (4) 3:4 | 9 |

155 | In the adjoining figure ( boldsymbol{A B}= ) ( 12 c m, C D=8 c m, B D=20 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 28 c. ( x ) has only one value and ( x geq 12 ) D. ( x ) cannot be determined with the given information | 10 |

156 | In ( triangle A B C, D ) is the midpoint of ( A B ) and ( E ) is mid point of AC. If area of ( triangle mathrm{ADE}=11 ) square units then area of ( triangle mathrm{ABC} ) is A. 33 square units B. 22 square units c. 44 square units D. None of the above | 10 |

157 | ( mathrm{PQ} ) | 10 |

158 | ( ln Delta L M N, angle L=60^{circ}, angle M=50^{circ} . ) If ( Delta L M N sim Delta P Q R, ) then the value of ( angle R ) is A ( cdot 40^{circ} ) B. 30 ( c cdot 70 ) D. ( 110^{circ} ) | 10 |

159 | 70. In a triangle, if three altitudes are equal, then the triangle is (1) Obtuse (2) Equilateral (3) Right (4) Isosceles | 9 |

160 | In the given figure, ( boldsymbol{A} boldsymbol{E} | boldsymbol{D} boldsymbol{B}, boldsymbol{B C}= ) ( mathbf{7} boldsymbol{c m}, boldsymbol{B} boldsymbol{D}=mathbf{5} boldsymbol{c m}, boldsymbol{D} boldsymbol{C}=mathbf{4} boldsymbol{c m} . ) If ( boldsymbol{C} boldsymbol{E}= ) ( 12 c m, ) find ( A E ) and ( A C ) | 10 |

161 | Fill in the blank. Two circles are congruent if | 9 |

162 | In the figure above, ( A C=6 ) and ( B C= ) 3. Point ( P(text { not shown }) ) lies on ( A B ) between ( A ) and ( B ) such that ( C P perp A B ) Which of the following could be the length of ( C P ? ) ( A cdot 2 ) B. 4 ( c .5 ) D. ( E ) | 10 |

163 | If the ratio of areas of two similar triangle is 16: 81 find the ratio of their corresponding sides. | 10 |

164 | In the figure, ( D E | B C ) (i) Prove that ( triangle A D E ) and ( triangle A B C ) are ( operatorname{similar} ) | 10 |

165 | n Fig., ( D E F G ) is a square in a triangle ( A B C ) right angled at ( A ) Prove that ( Delta A G F sim Delta D B G ) ii) ( Delta A G F sim Delta E F C ) | 10 |

166 | ngiven figure, ( frac{A O}{O C}=frac{B O}{O D}=frac{1}{2} ) and ( A B=5 mathrm{cm} . ) Find the value of DC. | 10 |

167 | In the given figure, ( A B | ) EF ( | ) CD. If ( A B= ) ( 22.5 mathrm{cm}, mathrm{EP}=7.5 mathrm{cm}, mathrm{PC}=15 mathrm{cm} ) and DC ( =27 mathrm{cm} . ) Find ( mathrm{AC} ) ( A cdot A C=37.5 mathrm{cm} ) B. AC = 22.5 cm ( c cdot A C=13.5 mathrm{cm} ) D. ( A C=27 mathrm{cm} ) | 10 |

168 | Find the value of ( x ) when ( D E | A B ) A. 8 ( B ) ( c cdot 16 ) D. none | 10 |

169 | If ( D ) is a point on side ( A B ) of ( A B C ) and ( D E ) is a line through D meeting ( A C ) at ( E ) such that ( Delta A D E sim Delta A C B . ) Then ( A B ) AD is equal to A . AE. AC B. AC. DE c. AE. BC D. AB. BC | 10 |

170 | A man of height ( 1.8 m ) is standing near a Pyramid. If the shadow of the man is of length ( 2.7 m ) and the shadow of the Pyramid is ( 210 m ) long at that instant, find the height of the Pyramid | 10 |

171 | In given figure ( P ) and ( Q ) are points on sides ( A B ) and ( A C ) respectively of ( triangle A B C ) If ( A P=3 mathrm{cm}, P B=6 mathrm{cm}, A Q=5 mathrm{cm} ) and ( mathrm{QC}=10 mathrm{cm}, ) show that ( mathrm{BC}=3 mathrm{PQ} ) | 10 |

172 | The areas of two similar triangles are ( 81 mathrm{cm}^{2} ) and ( 49 mathrm{cm}^{2} ) respectively. Find the ratio of their corresponding heights. What is the ratio of their corresponding medians? | 10 |

173 | One side of a right-angles triangular scarf is ( 80 mathrm{cm} ) and its longest side is 1 ( mathrm{m} . ) Find its cost at the rate of Rs 250 per ( boldsymbol{m}^{2} ) | 10 |

174 | In the trapezium ( A B C D, ) side ( A B | ) side DC. Diagonals ( A C ) and DB intersect each other at ( 0 . ) If ( A B=15, D C=10 ) find ( frac{O C}{O A} ) A ( cdot frac{O C}{O A}=frac{1}{3} ) в. ( frac{O C}{O A}=frac{7}{3} ) c. ( frac{O C}{O A}=frac{2}{3} ) D. ( frac{O C}{O A}=frac{5}{3} ) | 10 |

175 | Show that ( triangle A B C, ) where ( boldsymbol{A}(-mathbf{2}, mathbf{0}), boldsymbol{B}(mathbf{2}, mathbf{0}), boldsymbol{C}(mathbf{0}, mathbf{2}) ) and ( triangle boldsymbol{P} boldsymbol{Q} boldsymbol{R} ) where ( boldsymbol{P}(-mathbf{4}, mathbf{0}), boldsymbol{Q}(mathbf{4}, mathbf{0}), boldsymbol{R}(mathbf{0}, mathbf{4}) ) are similar. | 10 |

176 | In the figure given, if ( D E | B C ) and ( boldsymbol{A B}=mathbf{5} boldsymbol{x}-mathbf{4}, boldsymbol{B} boldsymbol{D}=mathbf{7} boldsymbol{x}-mathbf{5}, boldsymbol{C} boldsymbol{E}= ) ( 5 x-3 ) and ( A D=3 x-2, ) find the value of ( x ) 4 B. c. ( frac{7}{10} ) ” ( frac{9}{10} ) | 10 |

177 | ABCD a parallelogram. ( boldsymbol{E} ) is a point on ( A D ) and ( C E ) is produced to meet ( B A ) at ( F . ) If ( A E=4 c m, A F=8 mathrm{cm} ) and ( A B=12 mathrm{cm} . ) Find the perimeter (in ( mathrm{cm} ) of parallelogram ( boldsymbol{A B C D} ) | 10 |

178 | In the given figure, the triangles are congruent, Find the values of ( x ) and ( y ) | 9 |

179 | The perimeters of two similar triangles are ( 25 mathrm{cm} ) and ( 15 mathrm{cm} ) respectively. If one side of first triangle is ( 9 mathrm{cm}, ) then the corresponding side of the other triangle is ( A cdot 6.2 mathrm{cm} ) B. ( 3.4 mathrm{cm} ) c. ( 5.4 mathrm{cm} ) D. ( 8.4 mathrm{cm} ) | 10 |

180 | If the corresponding sides of two triangles are proportional, then the two triangles are similar by which test ( A cdot ) SSS test B. SAS test C. AAA test D. ASA test | 10 |

181 | We have seen how we can draw a series of right triangles as in the picture. What are the lengths of the sides the tenth triangle? | 10 |

182 | 67. The length (in metres) of the long- est rod that can be put in a room of dimensions 10 m x 10 mx 5 m is (1) 15/3 (2) 15 (3) 102 (4) 573 | 9 |

183 | If the corresponding angles of two triangles are equal then they are always congruent. The given statement A . Is always true B. Is always false c. can be true D. can be determined | 9 |

184 | Use the following figure to find ( A E ), if ( B D=4.1 mathrm{cm} ) A . ( 4.1 mathrm{cm} ) B. ( 8.2 mathrm{cm} ) c. ( 16.4 mathrm{cm} ) D. Data insufficient | 10 |

185 | ( Delta A B C sim ) 4. ( Delta Q P R ) 8. ( Delta P Q R ) c. ( Delta R P Q ) D. ( Delta P R Q ) | 10 |

186 | State whether the following statement is true or false. If two squares have equal areas, they | 9 |

187 | If ( A B C ) and DEF are similar triangles such that ( angle A=47^{circ} ) and ( angle B=83^{circ} ) then ( angle boldsymbol{F} ) is ( mathbf{A} cdot 60^{circ} ) B. ( 70^{circ} ) ( c .50^{circ} ) D. ( 100^{circ} ) | 10 |

188 | The perimeter of a triangle is equal to ( boldsymbol{K} ) times the sum of its altitude, then ( boldsymbol{K} ) is: ( mathbf{A} cdot mathbf{1} ) B. any number c. less than 1 D. greater than 1 | 10 |

189 | In the figure, seg ( P S ) intersects ( operatorname{seg} T K ) in the point ( R . angle T ) and ( angle K ) are right angles. State whether ( triangle P T R ) and ( triangle S K R ) are similar. If yes, by which test? | 10 |

190 | 62. The area of the triangle, formed by the graph of ax + by = 0 (where a, b are two positive real numbers) and the co-ordinate axes, is (1) sq. unit sq. unit sq. unit sq. unit | 9 |

191 | How many trapezoids congruent to this one: are there in the following diagram? ( A cdot 8 ) B. 12 ( c cdot 16 ) D. 2 | 9 |

192 | State true or false: With reference to the figure, ( R ) is mid-point of ( B C ) A. True B. False | 10 |

193 | If in ( triangle P Q R ) and ( triangle L M N, angle P=angle M= ) ( mathbf{6 0}^{circ}, boldsymbol{P Q}: boldsymbol{M} boldsymbol{L}=boldsymbol{P} boldsymbol{R}: boldsymbol{M} boldsymbol{N} ) and ( angle boldsymbol{N}= ) ( 55^{circ}, ) then ( angle Q ) is: A .50 B. 55 ( c cdot 65 ) D. 75 | 10 |

194 | Find the value of ( x ) of ( y ) using the information shown in the figure. Find the measure of ( angle A B D ) and ( angle A C D ) | 9 |

195 | In figure, ( P S ) is the bisector of ( angle Q P R ) of ( triangle P Q R ) Prove that ( frac{Q S}{S R}=frac{P Q}{P R} ) | 10 |

196 | Two triangles are similar, if their corresponding angles of two triangles areequal and corresponding sides are in the same ratio. Is it true? A. Yes B. Not of same size c. Not sure D. cannot be possible | 10 |

197 | 61. If the perimeter of a right-an- gled isosceles triangle is (4+2+4) cm, the length of the hypotenuse is : (1) 4 cm (2) 6 cm (3) 8 cm (4) 10 cm | 10 |

198 | For two figures to be congruent, they need to be: A. exactly alike B. smaller c. bigger D. none of these | 9 |

199 | In the figure given below, ( boldsymbol{C D} | boldsymbol{E} boldsymbol{F} ) ( A B . ) If ( A B=22.5 mathrm{cm}, E P=7.5 mathrm{cm} ) ( P C=15 mathrm{cm} ) and ( D C=27 ) m. Calculate ( boldsymbol{E} boldsymbol{F} ) A. ( E F=14.5 mathrm{cm} ) 3. ( E F=13.5 mathrm{cm} ) ( c . E F=12.5 mathrm{cm} ) Done of the above | 10 |

200 | The corresponding sides of two similar triangles are in the ratio ( 1: 3 . ) If the area of the smaller triangle in ( 40 mathrm{cm}^{2} ), find the area of the larger triangle. | 10 |

201 | If the bisector of an angle of a triangle bisects the opposite side, then prove that the triangle is isosceles. | 9 |

202 | A line segment DE is drawn parallel to base BC of ( Delta A B C ) which cuts AB at point ( mathrm{D} ) and ( mathrm{AC} ) at point ( mathrm{E} ). If ( mathrm{AB}=5 mathrm{BD} ) and ( mathrm{EC}=3.2 mathrm{cm} . ) Find the length of AE. A . ( 12.8 mathrm{cm} ) в. ( 1.28 mathrm{cm} ) c. ( 2.8 mathrm{cm} ) D. 12.6 ( mathrm{cm} ) | 10 |

203 | In triangle ( A B C, ) angle ( B ) is obtuse. ( D ) and ( E ) are mid-points of sides ( A B ) and ( B C ) respectively and ( F ) is a point on side ( A C ) such that ( E F ) is parallel to ( A B ) Then, ( B E F D ) is a parallelogram. State True or False. A. True B. False | 10 |

204 | State whether the following statement is true or false. All squares are congruent. A. True B. False | 9 |

205 | A man starts journey from home. He goes 5 kms to the North, then proceeds 10 kms to the right. From there he again turns right and goes 10 kms. How far is he from home? All distances are measured aerial- ly. (1) 200 (3) 225 (2) 150 (4) 1125 | 10 |

206 | condition is not considered for the similarity of triangle. A. ( S A S ) в. ( S S S ) c. ( A A A ) D. ( A S A ) | 10 |

207 | The sides of a triangle are ( 3 x+ ) ( 4 y, 4 x+3 y ) and ( 5 x+5 y ) units, where ( boldsymbol{x}, boldsymbol{y}>0 . ) The triangle is A. right angled B. equilateral c. obtuse angled D. none of these | 10 |

208 | The areas of two similar triangles ABC and PQR are ( 64 mathrm{cm}^{2} ) and ( 121 mathrm{cm}^{2} ) respectively. If ( Q R=15.4 mathrm{cm}, ) find ( B C ) | 10 |

209 | How many triangles are there in the following figure? 4.10 B . 24 ( c cdot 22 ) D. 20 | 10 |

210 | In given figure, ( D E | A C ) and ( D C | A P ) Prove that ( frac{boldsymbol{B} boldsymbol{E}}{boldsymbol{E C}}=frac{boldsymbol{B C}}{boldsymbol{C P}} ) | 10 |

211 | In the above figure, if DE ( | mathrm{BC} ), then ( x ) equals: ( A cdot 6 mathrm{cm} ) B. ( 7 mathrm{cm} ) ( c cdot 3 mathrm{cm} ) D. ( 4 mathrm{cm} ) | 10 |

212 | In the given figure, ( boldsymbol{A B} perp boldsymbol{B C}, boldsymbol{F G} perp ) ( B C ) and ( D E perp A C . ) Prove that ( triangle A D E ) ( sim triangle G C F ) | 10 |

213 | Find ( mathrm{BC} ), if ( mathrm{AB}=7.2 mathrm{cm} ) A. ( 7.2 mathrm{cm} ) B. ( 7.1 mathrm{cm} ) ( c cdot 0.72 mathrm{cm} ) D. ( 72 mathrm{cm} ) | 10 |

214 | State True or False. If false, give reasons for that If two triangles are congruent, their corresponding angle are equal A. True B. False | 9 |

215 | In triangle ( A B C ; M ) is mid-point of ( A B, N ) mid-point of ( A C ) and ( D ) is any point in base BC. Then: ( A . ) MN bisects AD B. MN divides AD in the ratio 1: 3 c. MN divides AD in the ratio 1: 2 D. MN divides AD in the ratio 1: 4 | 10 |

216 | In right angled ( Delta A B C angle B= ) ( 90^{circ} B D perp A C, A B=b, B D=c, B C= ) ( boldsymbol{a}, boldsymbol{A} boldsymbol{D}=boldsymbol{8} boldsymbol{D} boldsymbol{C}=mathbf{1 0} . ) Then find ( ^{boldsymbol{}} boldsymbol{b}^{prime} ) A ( cdot sqrt{5} ) B. 12 ( c cdot 6 sqrt{6} ) D. ( sqrt{18} ) | 10 |

217 | ( 4 mathrm{CR}=mathrm{AB} ) If the above statement is true then mention answer as 1 , else mention 0 if false | 10 |

218 | In the given ( Delta A B C, ) if ( A B=A C ) and ( B D=D C, ) then ( angle A D C= ) ( mathbf{A} cdot 60^{circ} ) B. ( 120^{circ} ) ( mathbf{c} cdot 90^{circ} ) D. ( 45^{circ} ) | 10 |

219 | Which of the following numbers form pythagorean triplet? ¡) 2,3,4 ii) 6,8,10 iii) 9,10,11 iv) 8,15,17 A . (ii), (iv) B. (i), (ii) c. (i), (ii), (iii) D. (ii), (iii) | 10 |

220 | In a ( triangle A B C ) BD and ( mathrm{CE} ) are the altitudes Prove that ( triangle A D B ) and ( triangle A E C ) are similar. Check whether ( triangle C D B ) and ( triangle B E C ) are similar | 10 |

221 | 64. In the adjoining figure if m ZABC = m ZACE, then A ABC is : D (1) right-angled (2) isosceles (3) equilateral (4) obtuse-angled | 9 |

222 | f ( triangle boldsymbol{P} boldsymbol{Q} boldsymbol{R} cong triangle boldsymbol{C} boldsymbol{A} boldsymbol{B}, boldsymbol{P} boldsymbol{Q}=boldsymbol{C} boldsymbol{A} . ) If true enter 1 else 0 | 9 |

223 | For a ( Delta A B C, A B=4 mathrm{mm}, B C=5 ) ( mathrm{mm} ) and ( boldsymbol{A C}=mathbf{6} ) mm. If ( boldsymbol{Delta} boldsymbol{A} boldsymbol{B} boldsymbol{C} cong ) ( Delta D E F, ) then ( E F=_{-}- ) ( mathbf{A} cdot 4 mathrm{mm} ) B. ( 6 mathrm{mm} ) ( c .5 mathrm{mm} ) D. cannot be determined | 9 |

224 | In the given figure you find two triangles. Indicate whether the triangles are similar. Give reasons in support of your answer. | 10 |

225 | In figure, ( angle B A C=90^{circ} ) and ( A D perp B C ) Then ( mathbf{A} cdot B D cdot C D=B C^{2} ) B. ( A B . A C=B C^{2} ) c. ( B D . C D=A D^{2} ) D. ( A B . A C=A D^{2} ) | 10 |

226 | Triangle ( X Y Z ) is right-angled at vertex ( Z . ) Calculate the length of ( Y Z, ) if ( X Y= ) ( 13 mathrm{cm} ) and ( X Z=12 mathrm{cm} ) | 10 |

227 | In the following figure, ( X Y ) is parallel to ( B C, A X=9 mathrm{cm} . X B=4.5 mathrm{cm} ) and ( B C=18 mathrm{cm} . ) Find ( X Y ) in cm. | 10 |

228 | In the figure ( : angle P S Q=90^{circ}, P Q= ) ( mathbf{1 0} c boldsymbol{m}, boldsymbol{Q} boldsymbol{S}=boldsymbol{6} boldsymbol{c m} ) and ( boldsymbol{R} boldsymbol{Q}=boldsymbol{9} boldsymbol{c m} ) Calculate the length of ( boldsymbol{P} boldsymbol{R} ) | 10 |

229 | The area of two similar triangles are in ratio ( 16: 81 . ) Find the ratio of its sides. A ( cdot frac{1}{9} ) в. ( frac{2}{9} ) ( c cdot frac{3}{9} ) D. ( frac{4}{9} ) | 10 |

230 | ( P ) and ( Q ) are the mid points on the sides ( C A ) and ( C B ) respectively of triangle ( A B C ) right angled at ( C . ) Prove that ( 4left(A Q^{2}+B P^{2}right)=5 A B^{2} ) | 10 |

231 | Consider the following statements: i) If three sides of a triangle are equal to three sides of another triangle, then the triangles are congruent. ii) If the three angles of a triangle are equal to three angles of another triangle respectively, then the two triangles are congruent. A . (i) is correct and (ii) is false B. Both (i) and (ii) are false c. Both (i) and (ii) are correct D. (i) is false and (ii) is correct | 9 |

232 | If altitudes ( mathrm{CE} ) and ( mathrm{BD} ) of a triangle ( mathrm{ABC} ) are equal, then ( A B=dots ) A . AC B. сE ( c . ) ВD D. BC | 10 |

233 | The given figure shows a parallelogram ABCD.E is a point in ( A D ) and ( C E ) produced meets BA produced at point ( F ) If ( A E=4 c m, A F=8 mathrm{cm} ) and ( A B=12 ) cm. find the perimeter of the parallelogram ABCD. ( A cdot 48 mathrm{cm} ) B. ( 44 mathrm{cm} ) ( c .60 mathrm{cm} ) D. ( 50 mathrm{cm} ) E . ( 45 mathrm{cm} ) ( F .54 mathrm{cm} ) G. none of the above | 10 |

234 | In the following figure,’ ( P^{prime} ) is point equidistance from two lines ( ^{prime} l^{prime} ) and ( ^{prime} m^{prime} ) intersecting at point ( ^{prime} A^{prime} . ) Show that the line ( A P ) bisect the angle between them. | 9 |

235 | n fig, ( A B C D ) is a parallelogram and ( B C ) is produced to a point ( Q ) such that ( boldsymbol{A D}=boldsymbol{C Q} . ) If ( boldsymbol{A Q} ) intersect ( boldsymbol{D} boldsymbol{C} ) at ( boldsymbol{P} ) show that ( a r(B P C)=a r(D P Q) ) | 9 |

236 | n fig., ( C M ) and ( R N ) are respectively then medians of ( triangle A B C ) and ( triangle P Q R ) prove that: ( triangle A M C sim triangle P N R ) | 10 |

237 | In the given triangle, ( A B ) is parallel to ( boldsymbol{P Q} cdot boldsymbol{A P}=boldsymbol{c}, boldsymbol{P C}=boldsymbol{b}, boldsymbol{P Q}=boldsymbol{a}, boldsymbol{A B}=boldsymbol{x} ) What is the value of ( x ? ) A・ ( x=a-frac{a c}{b} ) B. ( x=b+frac{a c}{b} ) c. ( x=b-frac{a c}{b} ) D. ( x=a+frac{a c}{b} ) | 10 |

238 | If both the rectangles are similar, find ( x ) ( A ) B. ( c ) D. none of the above | 10 |

239 | n right triangle ( A B C ), right-angled at ( C, M ) is the mid-point of hypotenuse ( A B . C ) is joined to ( M ) and produced to a point ( D ) such that ( D M=C M . ) Point ( D ) is joined to point ( B ).Which of the following is correct. This question has multiple correct options | 9 |

240 | Give two different examples of pair of (i) similar figures | 10 |

241 | The given figure shows a parallelogram ( A B C D ) with area ( 324 s q . c m . P ) is a point in ( A B ) such that ( A P: P B=1: 2 ) Find:the ratio ( O P: O D ) 4: 3 в. 2: ( c cdot 1: 4 ) D. 4: 3 | 10 |

242 | 73. In the given figures, the lengths of the sides of AABC and APOR are given and they are given in same units. Also ZA and ZB are given. Then value of ZP is 3.2 3.8 800 60° 60° B6 C 7.6 P12 (1) 42° (2) 36° (3) 38° (4) 40° | 10 |

243 | If ( angle D cong angle B ) and ( angle B cong angle Q, ) then ( angle D cong ) ( angle Q ) is a ( —— ) property of congruence. A. reflexive B. transitive c. symmetric D. addition postulate | 9 |

244 | Which of the following is a pythagorean triplet? в. (5,7,9) ( mathbf{D} cdot(8,15,17) ) | 10 |

245 | The diagonal BD of parallelogram ABCD intersects ( A E ) at ‘F’.’ E’ is any point on BC. Prove that DE.EF = FB. FA | 10 |

246 | f DE ( | ) BC and ( A D=1.7 c m, A B= ) ( 6.8 c m ) and ( A C=9 c m . ) Then length of AE is A . ( 2.25 mathrm{cm} ) B. ( 4.5 mathrm{cm} ) ( c .3 .4 mathrm{cm} ) D. ( 5.1 mathrm{cm} ) | 10 |

247 | Which of the following is a Pythagorean triplet? A. 3,4,5 в. 5,12,14 c. 6,8,11 D. 8,5,17 | 10 |

248 | At a certain time of the day, a man 6 feet tall, casts his shadow 8 feet long. Find the length of the shadow cast by a building 45 feet high, at the same time which is next to the man | 10 |

249 | If two non-parallel lines are perpendicular to two other straight lines, each to each. Show that the acute angle between the first pair of lines is equal to the acute angle between the second pair of lines. | 9 |

250 | State true or false: In quadrilateral ( A B C D, A D=B C ) and the diagonals ( A C ) and ( B D ) intersect at point ( boldsymbol{O}, ) such that ( frac{boldsymbol{O} boldsymbol{C}}{boldsymbol{O} boldsymbol{A}}=frac{boldsymbol{O} boldsymbol{D}}{boldsymbol{O B}}=frac{1}{mathbf{3}}, ) then the quadrilateral ( A B C D ) is a trapezium. A. True B. False | 10 |

251 | In ( triangle mathrm{PQR}, mathrm{M} ) and ( mathrm{N} ) are points on sides PQ and PR respectively such that PM = ( 15 mathrm{cm} ) and ( mathrm{NR}=8 mathrm{cm} . ) If ( mathrm{PQ}=25 mathrm{cm} ) and ( P R=20 mathrm{cm} ) state whether MN ( | mathrm{QR} ) | 10 |

252 | ( A B C ) and ( D B C ) are two isosceles triangles on the same base ( B C . ) Then ( angle A B D=angle A C D ) A. True B. False | 10 |

253 | If two triangles are ( _{–}- ) they are similar. A. Not equal B. Equiangular c. Different D. Not proportionate | 10 |

254 | fthree or more parallel lines are intersected by two transversals prove that the intercepts made by them on the transversals are proportional | 10 |

255 | Find the ( x ) in terms of ( a, b, c ) | 10 |

256 | ( ln triangle A B C ) is ( angle B ) is right angle. If ( a=16 ) and ( c=12 ) then ( b= ) A . 8 B . 18 c. 20 D . 28 | 10 |

257 | Fill in the blanks to make the statements true, In right triangle, the hypotenuse is the side | 9 |

258 | 70. The circumcentre of a right-an- gled triangle lies (1) at the right angular vertex (2) within the triangle (3) outside the triangle (4) on its hypotenuse | 9 |

259 | In a triangle ( A B C ), a straight line parallel to ( B C ) intersects ( A B ) and ( A C ) at point ( D ) and ( E ) respectively. If the area of ( A D E ) is one-fifth of the area of ( A B C ) and ( B C=10 mathrm{cm}, ) then ( D E ) equals A . ( 2 mathrm{cm} ) в. ( 2 sqrt{5} ) ст ( c .4 mathrm{cm} ) D. ( 4 sqrt{5} mathrm{cm} ) | 10 |

260 | 69. If the perimeter of a right-an- gled triangle is 56 cm and area of the triangle is 84 sq. cm, then the length of the hypote- nuse is (in cm) (1) 25 (2) 50 (3) 7 (4) 24 | 9 |

261 | n figure 2 , if ( D E | B C ), then the value of ( x ) is equal to ( A cdot 3 mathrm{cm} ) B. ( 4 mathrm{cm} ) ( c cdot 7 c m ) D. ( 4.7 mathrm{cm} ) | 10 |

262 | n the given fig 0 is a point in the nterior of a triangle of a triangle ( A B C, O D perp B C, O E perp A C ) and ( O F perp A B ) show that ( mathbf{O} mathbf{A}^{2}+mathbf{O B}^{2}+mathbf{O C}^{2}-mathbf{O D}^{2}-mathbf{O E}^{2}- ) ( mathrm{OF}^{2}=mathrm{AF}^{2}+mathrm{BD}^{2}+mathrm{CE}^{2} ) | 10 |

263 | n given figure ( D ) and ( E ) are respectively the points on the sides ( A B ) and ( A C ) of a ( triangle A B C ) such that ( A B=5.6 mathrm{cm}, A D= ) 1.4 ( c m, A C=7.2 mathrm{cm} ) and ( A E=1.8 mathrm{cm} ) show that ( D E | B C ) | 10 |

264 | f ( triangle A B C sim triangle A D E ) and ar ( (triangle A D E)= ) ( 9 operatorname{ar}(triangle A B C) ) then ( frac{B C}{D E} ) is equal to ( A ) B. 1 ( c cdot frac{3}{4} ) D. None of these | 10 |

265 | ( ln triangle D E F, ) Line PQ ( | ) side EF. Find DP. ( boldsymbol{D} boldsymbol{Q}=mathbf{1 . 8} mathrm{cm}, boldsymbol{Q} boldsymbol{F}=mathbf{5} . boldsymbol{4} mathrm{cm}, boldsymbol{E} boldsymbol{P}=mathbf{7 . 2} ) ( mathrm{cm} ) A ( .2 .4 mathrm{cm} ) B. ( 4.2 mathrm{cm} ) ( c .3 .5 mathrm{cm} ) D. ( 1.8 mathrm{cm} ) | 10 |

266 | ( triangle boldsymbol{A B C}, boldsymbol{X} boldsymbol{Y} | boldsymbol{B C}, frac{boldsymbol{A} boldsymbol{Y}}{boldsymbol{C Y}}=frac{1}{2} ) and ( A X=4 . ) Find ( B X ) | 10 |

267 | Line segment ( A B ) is parallel to another ine-segment ( C D, O ) is the midpoint of AD.Show that ( triangle A O B cong triangle D O C ) | 9 |

268 | Choose the correct criteria to prove that two triangles are congruent: Criteria: A) All three corresponding sides are congruent. B) Two angles and the side between them are congruent. C) Two angles and a non-included side are congruent. D) Two sides and the angle between them are congruent. For the given congruency theorem which option is suitable. 1) SSS (side-side-side) = 2) SAS (side-angle-side) = 3) AAS (angle-angle-side) = 4) ASA (angle-side-angle) ) = | 9 |

269 | In the figure, the line segment ( X Y ) is parallel to the side ( A C ) of ( triangle A B C ) and it divides the triangle into two parts of equal areas, then match the column. | 10 |

270 | In the figure, ( A P=3 mathrm{cm}, A R= ) ( 4.5 mathrm{cm}, A Q=6 mathrm{cm}, A B=5 mathrm{cm}, ) and ( A C=10 mathrm{cm} . ) Find the length (in ( mathrm{cm} ) ) of ( boldsymbol{A D} ) | 10 |

271 | State true or false: In parallelogram ( A B C D . E ) is the mid- point of ( A B ) and ( A P ) is parallel to ( E C ) which meets ( D C ) at point ( O ) and ( B C ) produced at ( boldsymbol{P} ). Hence ( O ) is mid-point of ( boldsymbol{A} boldsymbol{P} ) A. True B. False | 10 |

272 | An insect ( 8 m ) away from the foot of a lamp post which is ( 6 m ) tall, crawls towards it. After moving through a distance, its distance from the top of the lamp post is equal to the distance it has moved. How far is the insect away from the foot of the lamp post? [Bhaskaracharya’s Leelavathi] | 10 |

273 | 70. If one of the equal angles of an isosceles triangle is 65°, then the angle at the vertex is (1) 70° (2) 50° (3) 60° (4) 40° | 9 |

274 | 61. The point of intersection of the altitudes of a triangle is known as (1) Centroid (2) In-centre (3) Orthocentre (4) Circumcentre | 9 |

275 | Show that ( left(boldsymbol{m}^{2}-mathbf{1}right),(boldsymbol{2 m}), boldsymbol{m}^{2}+mathbf{1} ) always form a pythagoran triplet. | 10 |

276 | STATEMENT – 1: If tangents OR, PR, PQ and drawn respectively at ( A, B, C ) to the circle circumscribing an acute-angled ( Delta A B C ) so as the form another ( Delta P Q R ) then the ( angle R P Q=angle B A C ) STATEMENT – 2: ( Delta A B C ) is similar to ( Delta ) CPB. A. Statement – 1 is True, Statement – 2 is True, Statement 2 is a correct explanation for Statement – 1 B. Statement-1 is True, Statement – 2 is True : Statement 2 is NOT a correct explanation for Statement- – c. Statement – 1 is True, Statement- – 2 is False D. Statement-1 is False, Statement – 2 is True | 10 |

277 | 71. The heights of two similar right- angled triangles A LMN and A OPG are 48 cm and 36 cm. If OP = 12 cm, then LM is (1) 10/6 1 3 cm (2) 16 cm (3) 20 cm (4) 12 cm | 10 |

278 | 67. In two similar triangles ABC and MNP, if AB = 2.25 cm, MP = 4.5 cm and PN = 7.5 cm and m ZACB = m ZMNP and m ZABC = m ZMPN, then the length of side BC, in cm, is (1) 4.5 (2) 3.75 (3) 4.75 (4) 3.5 | 10 |

279 | ( P ) is a point on side ( B C ) of ( a ) parallelogram ABCD. If DP produced meets ( A B ) produced at point ( L ), then ( D L: D P=A L: B C ) If the above statement is true then mention answer as 1 , else mention 0 if false | 10 |

280 | 55. On decreasing each side of an equilateral triangle by 2 cm, there is a decrease of 4 13 cm2 in its area. The length of each side of the triangle is (1) 8 cm (2) 3 cm (3) 5 cm (4) 6 cm | 10 |

281 | Two triangles are ……….. if two angles and included side (common to both the angles) are equal to two angles and included side (common to both angles) of the other triangle. A. unequal B. congruent c. equilateral D. none of these | 9 |

282 | In given figure, If PSIIQR, prove that ( triangle P O S sim triangle R O Q ) | 10 |

283 | n ( triangle A B C, angle A B C=90^{circ}, A D= ) ( D C, A B=12 mathrm{cm} ) and ( B C=6.5 mathrm{cm} ) Find the area of ( triangle A D B ) | 10 |

284 | If ( Delta A B C cong Delta D E F, angle A=47^{circ}, angle E= ) ( 83^{circ}, ) then the value of ( angle C ) is: A ( cdot 47^{circ} ) B. 30 c. 40 ( D cdot 50^{circ} ) | 9 |

285 | “If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent”. Is the statementt true? Why? | 9 |

286 | If ( tan theta=frac{3}{4} ) Find ( 3 cos A+4 sin A ) | 10 |

287 | In two right triangles one side and an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent. | 9 |

288 | If ( boldsymbol{L} boldsymbol{M} | boldsymbol{Q} boldsymbol{R}, frac{boldsymbol{P} boldsymbol{L}}{boldsymbol{L} boldsymbol{Q}}=frac{boldsymbol{3}}{mathbf{5}}, boldsymbol{P} boldsymbol{R}=mathbf{5 . 6} boldsymbol{c m} ) then ( P M ) is A ( .2 .4 mathrm{cm} ) B. 2.3 ст ( c .2 .1 mathrm{cm} ) D. 2.2 cm | 10 |

289 | In the triangle ( A B C, P Q ) is parallel to ( B C . ) Find the length of ( x ) and ( y ) A. ( x=26.25, y=17.1 ) B. ( x=17.1, y=26.25 ) c. ( x=17.34, y=26.57 ) D. ( x=26.45, y=17.33 ) | 10 |

290 | In triangle ( P Q R L P=110^{circ} ) and ( L R= ) ( 60^{circ} ) which side of the triangle is smallest. | 10 |

291 | ( A C^{2}=B C times A B ) If the above statement is true then mention answer as 1 , else mention 0 if false | 10 |

292 | If the ratio of the corresponding sides of two similar triangles is 2: 3 then the ratio of their corresponding altitude is A. 3: 5 B. 16: 81 ( c cdot 4: 9 ) D. 2:3 | 10 |

293 | In the following figure, ABCD is a parallelogram.If ( angle A B P=x angle C B P ),then find the value of ( boldsymbol{x} ) | 10 |

294 | n given figure, ( D ) is a point on the side ( B C ) of ( triangle A B C ) such that ( angle B A C= ) ( angle A D C ) prove that ( boldsymbol{C A}^{2}=boldsymbol{C B} times boldsymbol{C D} ) | 10 |

295 | In the given figure ( Delta A B C cong Delta A B T ) write all the corresponding sides. | 9 |

296 | 66. ABCD is a rhombus. A straight line through C cuts AD produced at P and AB produced at 9. If DP = AB, then the ratio of the lengths of B9 and AB is (1) 2:1 (2) 1:2 (3) 1:1 (4) 3:1 | 10 |

297 | In triangle ( A B C ) is right-angled at ( B ) and ( B D ) is perpendicular to ( A C, ) then find: ( cot angle D B A ) is ( frac{m}{12} . ) value of ( mathrm{m} ) is, | 10 |

298 | Find the value of ( c ) in the triangle using Pythagoras theorem. A .24 B. 25 ( c .26 ) 0.2 | 10 |

299 | n the given figure ( A B C ) is a triangle. If ( frac{A D}{A B}=frac{A E}{A C}, ) then prove that DE II BC | 10 |

300 | State true or false: In an acute-angled ( triangle A B C, A D ) is perpendicular to side ( B C, ) then ( A C^{2}= ) ( A B^{2}+B C^{2}-2 B C times B D ) A. True B. False | 10 |

301 | triangles become always similar. A. Acute-angled B. Equilateral c. obtuse-angled D. None of the above | 10 |

302 | ( S ) and ( T ) are points on sides ( P R ) and ( Q R ) of ( triangle P Q R ) such that ( angle P=angle R T S . ) Show that ( triangle boldsymbol{R} boldsymbol{P} boldsymbol{Q} sim triangle boldsymbol{R} boldsymbol{T} boldsymbol{S} ) | 10 |

303 | ( mathrm{DE}=2.4 mathrm{cm}, ) find the length of BC | 10 |

304 | How many rectangles congruent to this rectangle are there in the following diagram? ( A cdot 6 ) B. 7 ( c cdot s ) D. 15 | 9 |

305 | Find the value of ( x ) and ( y ). (Use Pythagoras theorem) A ( . x=12 ) and ( y=3 ) 3. ( x=10 ) and ( y=5 ) c. ( x=12 ) and ( y=5 ) ( x=11 ) and ( y=5 ) | 10 |

306 | 17. Triangle is a. acute angled b. right angled but not isosceles c. isosceles d. isosceles right angled | 9 |

307 | A line parallel to the base of a triangle cuts the triangle into two regions of equal area. This line also cuts the altitude into two parts. Find the ratio of the two parts of the altitude. A . 1: 1 B. 1: 2 c. ( 1: sqrt{2} ) D. ( 1:(sqrt{2}+1) ) | 10 |

308 | ABCD is a quadrilateral; ( P, Q, R ) and ( S ) are the points of trisection of sides ( A B, B C, C D ) and DA respectively and are adjacent to A and C; prove thar PQRS is a parallelogram. | 10 |

309 | The sides of right angles triangle are 63,9 find its hypotenuse. | 10 |

310 | In the figure below, the diagonal ( boldsymbol{A C} ) of quadrilateral ( A B C D ) bisects ( angle B A D ) and ( angle B C D . ) Then ( B C=m D C ).Find ( m ) | 10 |

311 | n the following figure, ( X Y ) is parallel to ( B C, A X=9 mathrm{cm} . X B=4.5 mathrm{cm} ) and ( B C=18 mathrm{cm} ) What is the value of ( frac{A Y}{Y C} ? ) | 10 |

312 | In a triangle ( A B C, ) a line ( P Q ) is drawn parallel to ( B C ), points ( P ), Q being on ( A B ) and ( A C ) respectively. If ( A B=3 A P ) then what is the ratio of the area of triangle ( A P Q ) to the area of triangle ( A B C ? ) A .1: 3 B. 1: 5 c. 1: 7 D. 1: 9 | 10 |

313 | In the figure if ( D E | B C ) and ( A D= ) ( mathbf{3} boldsymbol{x}-mathbf{2}, boldsymbol{A} boldsymbol{E}=mathbf{5} boldsymbol{x}-mathbf{4}, boldsymbol{B} boldsymbol{D}=mathbf{7} boldsymbol{X}-mathbf{4} ) ( B D-7 x-5 ) AND ( C E=5 x-3 . ) Find ( mathbf{x} ) | 10 |

314 | In the following triplet pythagorean? show working (18,79,82) | 10 |

315 | 1. The sides of a triangle are 3x+4y, 4x+3y and 5x+5y wherex, y>0 then the triangle is [2002] (a) right angled (b) obtuse angled © equilateral (d) none of these | 10 |

316 | ( P M=4 mathrm{cm} ; Q M=4.5 mathrm{cm} ) ( P N=4 mathrm{cm} ; mathrm{NR}=4.5 mathrm{cm} ) | 10 |

317 | see how much time he would save taking a shortcut to home from football practice. He usually walked 6 blocks south and 9 blocks east. Which picture shows his shortcut? ( A ) B. ( c ) D. | 10 |

318 | In the given figure, ( D E | B C ) and ( A D: D B=5: 4, ) find ( frac{operatorname{area}(Delta D F E)}{operatorname{area}(Delta C F B)} ) 4. 5: 9 B . 25: 16 c. 25: 81 D. 81: 25 | 10 |

319 | In ( Delta A B C, angle A=90^{circ} ) and ( A D perp B C ) Then, ( boldsymbol{A} boldsymbol{D}^{3}=boldsymbol{B} boldsymbol{D} times boldsymbol{D} boldsymbol{C} ) A. True B. False | 10 |

320 | us- 54. It is given that AABC AFDE in which AB = 5cm, ZB= 40°, ZA= 80° and FD = 5cm. Then, which of the following is true? (1) ZD = 60° (2) ZE= 60° (3) ZF = 60° (4) ZD = 80° | 9 |

321 | ( mathrm{DE}=mathrm{FE} ) | 10 |

322 | 62. The circumcentre and the ortho- centre of a triangle coincide. Then (1) the centroid also coincides with them (2) the centroid will be different from them (3) the triangle is isosceles (4) the triangle is right angled | 9 |

323 | 61. The perimeters of two similar tri- angles are 30 cm and 20 cm re- spectively. If one side of the first triangle is 9 cm. Determine the corresponding side of the second triangle (1) 13.5 cm (2) 6 cm (3) 15 cm (4) 5 cm | 10 |

324 | If the area of two similar triangles are equal, then they are A . equilateral B. isosceles c. congruent D. not congruent | 10 |

325 | When one acute angle of a triangle is equal to one acute angle of other triangle, and the triangles are right angles, do you think the triangles are similar? A. Not sure B. Similar c. Not similar D. cannot be possible | 10 |

326 | If ( triangle A B C cong triangle R Q P, angle A=80^{circ}, angle B= ) ( 60^{circ}, ) then the value of ( angle P ) is A . ( 60^{circ} ) В. ( 50^{circ} ) c. ( 40^{circ} ) D. ( 80^{circ} ) | 10 |

327 | Given line ( A B ) is parallel to line ( C D ) ( angle C H G ) and ( angle E G B ) are: A. Non-congruent B. Congruent c. Complementary D. None of these | 9 |

328 | 63. In the figure A ACB – A APQ. If BC = 8 cm, PQ4 cm, AP 2.8 cm, find CA: (1) 8 cm (2) 6.5 cm (3) 5.6 cm (4) None of these | 10 |

329 | In triangle ( A B C, angle B=90^{circ} ) and ( D ) is the mid-point of side Be. Prove that: ( A C^{2}=A D^{2}+3 C D^{2} ) | 10 |

330 | ( operatorname{In} ) a trapezium ( boldsymbol{A B C D}, boldsymbol{A B} | boldsymbol{D C} ) and ( D C=2 A B . E F ) drawn parallel to ( A B ) cuts ( A D ) in ( F ) and ( B C ) in ( E ) such that ( frac{B E}{E C}=frac{3}{4} . ) Diagonal ( D B ) intersects ( E F ) at ( G . ) Prove that ( mathbf{7 F E}=mathbf{1 0 A B} ) | 10 |

331 | ? (4) 7.5 at 55. In A POR, PS is the bisector of ZP and PT I QR, then TPS is equal to : TS is (1)29+ ZR 2)909 + Ž 40 (3) 90° -5R (4) (29-ZR) | 10 |

332 | 68. In A ABC, AD is the internal bi- sector of ZA, meeting the side BC at D. If BD = 5 cm, BC = 7.5 cm, then AB : AC is (1) 2:1 (2) 1:2 (3) 4 : 5 (4) 3:5 | 10 |

333 | In the given figure, apply ( operatorname{sss} ) congruence condition and state the result in the symbolic form. | 10 |

334 | ( D ) is any point on side ( A C ) of a ( Delta A B C ) with ( A B=A C ) Show that ( C D<B D ) | 10 |

335 | In a right angled triangle, if the square of the hypotenuse is twice the product of the other two sides, then one of the angles of the triangle is: A ( cdot 15^{circ} ) B . ( 30^{circ} ) ( c cdot 45^{circ} ) D. ( 60^{circ} ) | 10 |

336 | In the figure below. PQR is a right- angle triangle right angled at ( Q . X Y ) is parallel to ( boldsymbol{Q} boldsymbol{R} . boldsymbol{P} boldsymbol{Q}=boldsymbol{6} mathrm{cm}, boldsymbol{P Y}=mathbf{4} mathrm{cm} ) and ( P X: X Q=1: 2 . ) Calculate the lengths of ( boldsymbol{P R} ) and ( boldsymbol{Q} boldsymbol{R} ) A. ( P R=12 mathrm{cm} ; Q R=10.392 mathrm{cm} ) B. ( P R=13 mathrm{cm} ; Q R=11.392 mathrm{cm} ) c. ( P R=11 mathrm{cm} ; Q R=12.392 mathrm{cm} ) D. none of the above | 10 |

337 | ( mathrm{BP}=2 mathrm{AC} ) f the above statement is true then mention answer as 1 , else mention 0 if false | 10 |

338 | ( triangle A B C, D E | B C, ) find the value of ( x ) | 10 |

339 | If an equilateral triangle, having centroid at the origin, has a side along the line, ( x+y=2 ), then the area (in sq.units) of this triangle is: ( mathbf{A} cdot mathbf{6} ) B. ( 6 sqrt{3} ) c. ( frac{9}{2} sqrt{3} ) D. ( 3 sqrt{6} ) | 9 |

340 | 69. O is the orthocentre of AABC. If ZBOC = 110°, ZBAC is equal to (1) 70° . (2) 80° (3) 110 (4) 90° | 9 |

341 | 86. The length of each side of an equi- lateral triangle is 1473 cm. The area of the incircle, in cm, is (1) 450 (2) 308 (3) 154 (4) 77 | 9 |

342 | In a ( triangle A B C, B C=A B ) and ( angle B=80^{0} ) Then ( angle A ) is equal to? A ( cdot 80^{circ} ) ( ^{0} 0 cdot 8 cdot 8^{00} ) B . ( 40^{circ} ) ( c cdot 50^{0} ) D. ( 100^{circ} ) | 10 |

343 | In ( triangle A B C, ) if ( A D perp B C ) and ( A D^{2}= ) ( B D times D C, ) prove that ( angle B A C=90^{0} ) | 10 |

344 | n given figure, ( angle B A C=90^{circ} ) and segment ( A D perp B C . ) Prove that ( A D^{2}= ) ( boldsymbol{B} boldsymbol{D} times boldsymbol{D} boldsymbol{C} ) | 10 |

345 | Anna went to the market to buy some boxes to store things. She was surprised to find boxes one inside the other. They were ( ldots ldots ) boxes. A. Not similar B. Ambiguous c. same size D. similar | 10 |

346 | f ( triangle boldsymbol{D} boldsymbol{E} boldsymbol{F} cong triangle boldsymbol{R} boldsymbol{P} Q, ) then ( angle boldsymbol{D}=angle boldsymbol{Q} . ) If true enter 1 else 0 | 9 |

347 | Let ( X ) be any point on the side ( B C ) of ( a ) triangle ABC. If ( mathrm{XM}, mathrm{XN} ) are drawn parallel to BA and CA meeting CA, BA in M, N respectively; MN meets BC produced in ( T, ) prove that ( boldsymbol{T} boldsymbol{X}^{2}=boldsymbol{T} boldsymbol{B} times ) ( boldsymbol{T} boldsymbol{C} ) | 10 |

348 | In ( triangle A B C, X Y | B C ) and ( X Y ) divides the triangle into two parts of equal areas. Find ( left(frac{B X}{A B}right) ) | 10 |

349 | Goldfish are sold at Rs.15 each. The rectangular coordinate graph showing the cost of 1 to 12 goldfish is: A. a straight line segment B. a set of horizontal parallel line segments c. a set of vertical parallel line segments D. a finite set of distinct points E a straight line | 10 |

350 | ( A B C D ) is a trapezium in which ( A B | ) ( D C, D C=7 c m ) distance between ( A B ) and ( D C ) is ( 4 c m ). Find ( A B ). | 10 |

351 | Check if the triangles are similar. If similar, write the similarity in symbolic form. Mention the similarity condition used ( mathbf{A} cdot A S A ) B. ( S A S ) ( c . A A S ) D. NONE | 10 |

352 | Under which congruence condition the following figure are said to be congruent: (a) Two Line Segments (b) Two squares (c)Two rectangles ( (d) ) Two circles | 9 |

353 | Solve the following: n ( Delta M N P, angle M N P= ) ( 90^{circ}, operatorname{seg} N Q perp operatorname{seg} M P . ) If ( M Q= ) ( mathbf{9}, boldsymbol{Q} boldsymbol{P}=mathbf{4}, ) then find ( boldsymbol{N} boldsymbol{Q} ) | 10 |

354 | In given figure the diagonal BD of a parallelogram ABCD intersects the segment AE at the point ( F ), where E is any point on the side BC. Prove that ( boldsymbol{D} boldsymbol{F} times boldsymbol{E} boldsymbol{F}=boldsymbol{F} boldsymbol{B} times boldsymbol{F} boldsymbol{A} ) | 10 |

355 | In given figures sides ( A B ) and ( A C ) and median ( A D ) of a triangle ( A B C ) are respectively proportional to sides ( boldsymbol{P Q} ) and ( P R ) and median ( P M ) of another triangle ( P Q R . ) Show that ( triangle A B C sim ) ( triangle boldsymbol{P} boldsymbol{Q} boldsymbol{R} ) | 10 |

356 | In triangle ( A B C, ) medians ( A D ) and ( B E ) are drawn.lf ( boldsymbol{A D}=mathbf{4}, angle boldsymbol{D A B}=frac{boldsymbol{pi}}{mathbf{6}} ) and ( angle A B E=frac{pi}{3}, ) then the area of the ( triangle A B C ) is A ( cdot frac{8}{3} ) в. ( frac{16}{3} ) c. ( frac{32}{3 sqrt{3}} ) D. ( frac{64}{3} ) | 10 |

357 | n the figure (1) given below, AB I CR and LM | QR Prove that ( frac{boldsymbol{B} boldsymbol{M}}{boldsymbol{M} boldsymbol{C}}=frac{boldsymbol{A} boldsymbol{L}}{boldsymbol{L} boldsymbol{Q}} ) | 10 |

358 | If in triangle ( boldsymbol{X} boldsymbol{Y} boldsymbol{Z}, boldsymbol{X} boldsymbol{Y}=boldsymbol{X} boldsymbol{Z} ) and ( M, N ) are the mid points of ( X Y, Y Z ) then which one of the following is correct? ( mathbf{A} cdot M N=Y Z ) в. ( N Y=N Z=M N ) c. ( M X=M Y=N Y ) D. ( M N=M X=M Y ) | 10 |

359 | n given figure, If ( boldsymbol{E} boldsymbol{F}|boldsymbol{D} boldsymbol{C}| boldsymbol{A} boldsymbol{B} ). prove that ( frac{boldsymbol{A} boldsymbol{E}}{boldsymbol{E} boldsymbol{D}}=frac{boldsymbol{B} boldsymbol{F}}{boldsymbol{F} boldsymbol{C}} ) | 10 |

360 | State whether the following statement is true or false. If two rectangles have equal area, they | 9 |

361 | Two triangles are congruent if they have the same and A. Not sure B. Shape c. Both B and D D. size | 9 |

362 | All congruent figures are similar but the similar figures are not congruent.Is this statement true or false? ( A ). False B. Both A and C c. True D. Not applicable | 10 |

363 | n the given figure, ( angle B=60^{circ}, A B=8 ) ( mathrm{cm} ) and ( mathrm{BC}=25 mathrm{cm} . ) Calculate : (i) ( B E ) (ii) ( boldsymbol{A C} ) | 10 |

364 | The perimeter of two similar triangles ( triangle A B C ) and ( triangle D E F ) are ( 36 mathrm{cm} ) and 24 ( mathrm{cm} ) respectively. If ( D E=10 mathrm{cm}, ) then ( A B ) is : A . ( 12 mathrm{cm} ) B. ( 20 mathrm{cm} ) c. ( 15 mathrm{cm} ) D. ( 18 mathrm{cm} ) | 10 |

365 | In the given figure you find two triangles. Indicate whether the triangles are similar. Give reasons in support of your answer. | 10 |

366 | In the adjoining figure, find the measure of ( angle B A C, ) if ( angle A B D=angle C A D ) and ( angle B A D=angle A C D ) A ( cdot 120^{circ} ) В. ( 60^{circ} ) ( c cdot 75^{circ} ) D. ( 90^{circ} ) | 10 |

367 | Prove that if the lengths of two altitudes of a triangle are equal, then the triangle is isosceles. | 10 |

368 | Which of the following postulate can be used to prove ( Delta K L M ) and ( Delta R S T ) are similar? This question has multiple correct options A . AAS B. sss c. sas D. AAA | 10 |

369 | Find ( x ) | 10 |

370 | A pole of 6 metres in height casts a shadow of 3.6 metres at a certain time of the day. Find the length of the shadow cast by a 4.5 metres tower at the same time. | 10 |

371 | In the figure ( angle A=angle C E D, C D= ) ( mathbf{8} boldsymbol{c m}, boldsymbol{C} boldsymbol{E}=mathbf{1 0} boldsymbol{c m}, boldsymbol{B} boldsymbol{E}= ) ( 2 c m, A B=9 c m, A D= ) ( b ) and ( D E=a ). The value of ( a+b ) is A. ( 13 mathrm{cm} ) В. ( 15 mathrm{cm} ) ( c cdot 12 mathrm{cm} ) D. ( 9 mathrm{cm} ) | 10 |

372 | State true or false: With reference to the figure, ( mathbf{2} boldsymbol{P} boldsymbol{R}=boldsymbol{A} boldsymbol{B}+boldsymbol{A} boldsymbol{C} ) A. True B. False | 10 |

373 | In figure, DE||BC, then the value of ( x ) equals to: A. ( 2.5 mathrm{cm} ) B. ( 2 mathrm{cm} ) c. ( 1.4 mathrm{cm} ) D. ( 4 mathrm{cm} ) | 10 |

374 | Fig. ( 6.36, frac{Q R}{Q S}=frac{Q T}{P R} ) and ( angle 1=angle 2 ) Show that ( Delta P Q S sim Delta T Q R ) | 10 |

375 | STATEMENT – 1: If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar. STATEMENT – 2 : If in two triangles, | 10 |

376 | If three sides of a triangle are respectively equal to three sides of another triangle, then the triangles are: A. unequal B. equilateral c. congruent D. none of these | 9 |

377 | Rhombus PQRB is inscribed in ( triangle boldsymbol{A B C} ) such that ( angle B ) is one of the its angle, ( P, Q ) and ( mathrm{R} ) lie on ( mathrm{AB}, mathrm{AC} ) and ( mathrm{BC} ) respectively. If ( A B=12 mathrm{cm} ) and ( B C=6 mathrm{cm} ) find the sides of rhombus PQRB. | 10 |

378 | 65. The ratio of circumradius and hypotenuse of a right-angled tri- angle is (1) 2:3 (2) 1:2 (3) 2:1 (4) 1:1 | 9 |

379 | In ( triangle boldsymbol{A B C} ) and ( triangle boldsymbol{D E F}, angle boldsymbol{B}=angle boldsymbol{E}= ) ( 90^{circ} ; A C=D F a n d B C=E F ) Then triangles are congruent. A. True B. False | 9 |

380 | In given figure ( A B C ) is a triangle in which ( A B=A C ) and ( D ) is a point on ( A C ) such that ( B C^{2}=A C times C D . ) Prove that ( mathrm{BD}=mathrm{BC} ) | 10 |

381 | 53. In the given figure, ZA = 80°, ZB = 60°, ZC = 2x and ZBDC = yº. BD and CD bisect angles B and C respectively. The values of x and y respectively are : BE (1) 15° and 70° (2) 10° and 160° (3) 20° and 130° (4) 20° and 125° | 10 |

382 | n ( triangle A B C ) and ( triangle P Q R, ) if ( A B= ) ( 2.5 c m, A C=3.5 c m, B C= ) ( 4.0 c m, P Q=5 c m, P R=7 c m ) and ( Q R=8 c m, ) then find whether ( triangle A B C ) and ( triangle P Q R ) are similar or not | 10 |

383 | For two acute angled ( triangle A B C ) and ( triangle P Q R ) if ( triangle A B C sim triangle P Q R ) then prove ( operatorname{that} frac{operatorname{area}(triangle A B C)}{operatorname{area}(triangle P Q R)}=frac{A B^{2}}{P Q^{2}}=frac{B C^{2}}{Q R^{2}}= ) ( frac{A C^{2}}{P R^{2}} ) | 10 |

384 | In the adjoining figure, D is a point on the side BC of ( Delta A B C ) such that ( angle A D C=angle B A C ) Then ( frac{C A}{C D}=frac{C B}{C A} ) A. True B. False | 10 |

385 | In a circle with centre ( boldsymbol{O}, boldsymbol{O} boldsymbol{D} perp ) chord ( A B . ) If ( B C ) is the diameter, then which of the following option is correct: ( mathbf{A} cdot A C=B C ) В ( . O D=B D ) c. ( A C=2 times O D ) D. None of these | 10 |

386 | If the areas of two similar triangles are equal, then they are A . equilateral B. isosceles c. congruent D. not congruent | 9 |

387 | PQR is a triangle right angled at ( P ) and M is a point on QR such that PM ( perp ) QR. Show that ( boldsymbol{P} boldsymbol{M}^{2}=boldsymbol{Q} boldsymbol{M} cdot boldsymbol{M} boldsymbol{R} ) | 10 |

388 | Corresponding sides of two similar triangles are in the ratio ( 2: 3 . ) If the area of the smaller triangle is ( 48 mathrm{cm}^{2} ) determine the area of the larger triangle. | 10 |

389 | If the area of two similar triangles are equal, prove that they are congruent. | 9 |

390 | In given figure, DEFG is a square and ( angle B A C=90^{0} . ) Prove that (i) ( triangle A G F sim triangle D B G ) (ii) ( triangle A G F sim triangle E F C ) (iii) ( triangle D B G sim triangle E F C ) ( (text { iv }) boldsymbol{D} boldsymbol{E}^{2}=boldsymbol{B} boldsymbol{D} times boldsymbol{E} boldsymbol{C} ) | 10 |

391 | 65. AABC is an isoscles triangle with AB = AC and ZA = x, if side BA is produced such that AB = AD then what will be the value of ZBCD? (1) 90° – X (2) 90° + x (3 90° (4) 2x | 9 |

392 | Two angles of triangle ( A B C ) are ( 85^{circ} ) and ( 65^{circ} ) while the two angles of another triangle DEF are ( 30^{circ} ) and ( 65^{circ} . ) Which of the statements is correct? A. ( triangle ) ABC is similar to ( triangle ) DEF B. ( triangle ) ABC is congurent to ( triangle ) DEF c. ( triangle ) ABC is equal to ( triangle ) DEF D. None of these | 10 |

393 | ( A B C ) and ( B D E ) are two equilateral triangles such that ( D ) is the midpoint of ( B C . ) Ratio of the areas of triangles ( A B C ) and ( B D E ) is A .2: 1 B. 1: 2 ( c cdot 4: 1 ) D. 1: 4 | 10 |

394 | n given figure, If ( triangle P O S sim triangle R O Q ) prove thar PSI|QR. | 10 |

395 | 60. In AABC, it is given that D is the midpoint of BC; E is the mid- point of BDand O is the midpoint of AE.Then, ar(ABOE) = ? B E D (1) ar(ABC) (2) artAABC (3) ar(ABC 14) ar(ABC | 9 |

396 | Find DF, if ( mathrm{CG}=11 mathrm{cm} ) A. ( 5.6 mathrm{cm} ) B. ( 5.5 mathrm{cm} ) ( c cdot 0.55 mathrm{cm} ) D. ( 55 mathrm{cm} ) | 10 |

397 | 58. I is the incentre of a triang ABC. If ZABC = 65° and ZACH = 55°. then the value of BIC is (1) 130° (3) 140° (2) 120° (4) 110 | 9 |

398 | If ( Delta A B C cong Delta X Y Z, ) which of the following statements is incorrect? ( mathbf{A} cdot angle A=angle X ) В. ( angle B=angle Z ) c. ( A B=X Y ) ( mathbf{D} cdot B C=Y Z ) | 9 |

399 | ( A B C D ) is a rectangle inscribed in a quadrant of a circle having radius 10cm. If ( A D=2 sqrt{5} c m ), find the area of ( A B C D ) ( A cdot 30 c m^{2} ) 3. ( 50 mathrm{cm}^{2} ) ( c cdot 40 c m^{2} ) D. ( 35 c m^{2} ) | 10 |

400 | In an equilateral triangle if 3 times the square of one side is equal to ( mathrm{K} ) times the square of its altitude then Kequals A ( cdot frac{4}{3} ) B. 2 ( c cdot 4 ) D. ( frac{9}{4} ) | 10 |

401 | 70. The lengths of three medians of a triangle are 9 cm, 12 cm and 15 cm. The area (in sq. cm) of the triangle is (1) 24 (2) 72 (3) 48 (4) 144 | 10 |

402 | n given figure, AD and CE are two altitudes of ( triangle A B C ). Prove that (i) ( triangle A E F sim triangle C D F ) (ii) ( triangle A B D sim triangle C B E ) (iii) ( triangle A E F sim triangle A D B ) (iv) ( triangle boldsymbol{F} boldsymbol{D} boldsymbol{C} sim triangle boldsymbol{B} boldsymbol{E} boldsymbol{C} ) | 10 |

403 | 57. In a triangle ABC, the sum of the exterior angles at B and C is equal to : (1) 180° + ZBAC (2) 180° – ZBAC (3) 180° + 1 ZBAC (4) 180° + 2 ZBAC | 9 |

404 | If the same photograph is printed in different sizes, we say it is A. Not similar B. Similar c. common D. None | 10 |

405 | ( A B C ) is a triangle in which ( angle B=2 angle C . D ) is a point on BC such that AD bisects ( angle B A C ) and ( A B=C D . ) Find ( angle B A C ) A ( .72^{circ} ) ( ^{0} ) B. ( 36^{circ} ) ( c cdot 108^{circ} ) D. ( 90^{circ} ) | 9 |

406 | One of the angles of a ( triangle ) is ( 75 . ) If the difference of the other two other is 35 Find the largest angle of the ( triangle ) | 9 |

407 | Hence, ( Delta A D C ) and ( Delta B A C ) are similar. If the above statement is true then mention answer as 1 , else mention 0 if false | 10 |

408 | n the figure ( Delta A B C, D E | ) ( B C, A(Delta A D E)=48 ) sq.cm., ( frac{A D}{D B}=frac{4}{5} ) Find the area of ( Delta B E C ) A . 60 sq.cm B. 95 sq.cm c. 108 sq.cm D. 135 sa.cm | 10 |

409 | ( D ) is a point on the side ( B C ) of a triangle ( A B C ) such that ( angle A D C=angle B A C ) Show that ( C A^{2}=C B . C D ) | 10 |

410 | n triangle ( A B C, angle B A C=90^{circ}, ) and ( A D ) is its bisector. If ( D E ) is drawn ( perp A C, ) prove that ( D E times(A B+A C)= ) ( boldsymbol{A B} times boldsymbol{A C} ) | 10 |

411 | If in ( triangle A B C ) and ( triangle D E F, frac{A B}{D E}=frac{B C}{F D} ) then they will be similar if A. ( angle B=angle E ) в. ( angle A=angle D ) c. ( angle B=angle D ) ( mathbf{D} cdot angle A=angle F ) | 10 |

412 | State Pythagoras theorem. | 10 |

413 | If two triangles are symmetric, then they are A . Equilateral B. congruent c. Equal D. Isosceles | 9 |

414 | The ratio of the area of two similar triangles is ( 9: 16, ) then the ratio of their corresponding sides will be | 10 |

415 | If ( Delta P Q R sim Delta X Y Z, angle Q=50^{circ} ) and ( angle R=70^{circ}, ) then the angle ( angle X+angle Y ) is equal to: A ( .70^{circ} ) B. 50 ( c cdot 120 ) D. ( 110^{circ} ) | 10 |

416 | In ( Delta A B C, angle A=30^{circ}, angle B=40^{circ} ) and ( angle C=110^{circ} ) ( ln Delta P Q R, angle P=30^{circ}, angle Q=40^{circ} ) and ( angle R=110^{circ} ) Then Is ( Delta A B C cong Delta P Q R ) by ( mathrm{AAA} ? ) A. True B. False | 9 |

417 | 59. The ratio of the areas of two isos- celes triangles having equal ver- tical angles is 1 : 4. The ratio of their heights will be (1) 1 : 2 (2) 3:4 (3) 2:3 (4) 6:7 | 10 |

418 | In given figure, ( P B ) and ( Q ) a are perpendiculars to segment AB. If PO=5 ( mathrm{cm}, mathrm{Q} mathrm{O}=7 mathrm{cm} ) and Area ( triangle boldsymbol{P O B}= ) ( 150 c m^{2} ) find the area of ( triangle Q O A ) | 10 |

419 | Prove that the line segments joining the midpoints of the sides of a triangle from four triangles each of which is similar to the original triangle. | 10 |

420 | If ( l, m, n ) are three parallel lines and the transversal ( t_{1} ) and ( t_{2} ) cut the lines ( l, m, n ) at the points ( A, B, C ) and ( P, O, R ) as shown in the figure, then A ( cdot frac{A B}{B C}=frac{P O}{O R} ) B. ( frac{A B}{O R}=frac{B C}{P O} ) c. ( frac{A P}{B O}=frac{B O}{C R} ) D. ( frac{A B}{P O}=frac{A P}{B O} ) | 10 |

421 | Which of the following statements is true when ( Delta A B C cong Delta D E F ) ( mathbf{A} cdot angle A=angle D ) B . ( angle A=angle E ) c. ( angle A=angle F ) D. none of these | 9 |

422 | In the given figure, ( 2 A P=5 P B ) and ( 2 C P=5 P D ) Then, ( Delta A C P ) and ( Delta B D P ) are similar. If the above statement is true then mention answer as 1 , else mention 0 if false. | 10 |

423 | f ( triangle A B C cong triangle P R Q ) then ( A B=P Q ).If true enter 1 else 0 | 9 |

424 | n given figure, IF ( angle A=angle C ), then prove that ( triangle A O B sim triangle C O D ) | 10 |

425 | ( triangle A B C sim triangle D E F . ) Explain whether the two similar triangles may be congruent as well. | 9 |

426 | n right triangle ( A B C, overline{D E} ) ( B C, C D=1.5, ) and ( B E=2.0 ) The sine of angle ( theta ) is equal to ( mathbf{A} cdot mathbf{1} ) 2 B. 3 4 ( c cdot frac{sqrt{2}}{2} ) ( frac{sqrt{3}}{2} ) E . 3 ( F ) | 10 |

427 | A right triangle has a hypotenuse of length ( p c m ) and one side of length ( q c m ) ( mathbf{f} p-boldsymbol{q}=1, ) find the length of the third side of the triangle if ( p=5 ) and ( q=4 ) | 10 |

428 | n given Figure, ( D E | B C . ) If ( A D= ) ( boldsymbol{x}, boldsymbol{D} boldsymbol{B}=boldsymbol{x}-boldsymbol{2}, boldsymbol{A} boldsymbol{E}=boldsymbol{x}+boldsymbol{2} ) and ( boldsymbol{E} boldsymbol{C}= ) ( x-1, ) find the value of ( x ) | 10 |

429 | If the area of two similar triangles are equal, then prove that they are congruent. | 10 |

430 | ( E ) and ( F ) are points on the sides ( P Q ) and ( P R ) respectively of a ( Delta P Q R ) For each of the following cases state whether ( boldsymbol{E F} | boldsymbol{Q} boldsymbol{R} ) (1) ( P E=3.9 c m, E Q=3 mathrm{cm}, P F= ) ( mathbf{3 . 6} ) cm and ( boldsymbol{F R}=mathbf{2 . 4} ) (2) ( P E=4 c m, Q E=4.5 mathrm{cm}, P F= ) ( 8 mathrm{cm} ) and ( R F=9 mathrm{cm} ) (3) ( P Q=1.28 mathrm{cm} mathrm{PR}= ) ( mathbf{2 . 5 6} mathbf{c m}, boldsymbol{P} boldsymbol{E}=mathbf{0 . 1 8} mathbf{c m} ) and ( boldsymbol{P} boldsymbol{F}= ) ( mathbf{0 . 3 6} c boldsymbol{m} ) | 10 |

431 | The same ratio of corresponding sides is referred to as the factor for polygons. ( A ). scale B. vernier c. similar D. congruence | 9 |

432 | Two angles of one triangle are ( 85^{circ} ) and ( 65^{circ} ) is equal to angles of the other. Are they similar? Prove it. | 10 |

433 | n given figure ( A B C D ) is a quadrilateral in which ( P, Q, R ) and ( S ) are mid-points of the sides. ( A B, B C, C D ) and ( D A . A C ) is a diagonal. Show that: (i) ( boldsymbol{S R} | boldsymbol{A C} ) and ( boldsymbol{S R}=frac{mathbf{1}}{mathbf{2}} boldsymbol{A C} ) (ii) ( boldsymbol{P Q}=boldsymbol{S} boldsymbol{R} ) (iii) ( P Q R S ) is a parallelogram | 10 |

434 | Which of the following statements are true (T) and which are false(F): The two altitudes corresponding to two equal sides of a triangle need not be equal. | 10 |

435 | ( triangle P Q R ) is right angled at ( Q, Q X perp ) ( boldsymbol{P R}, boldsymbol{X} boldsymbol{Y} perp boldsymbol{R} boldsymbol{Q} ) and ( boldsymbol{X} boldsymbol{Z} perp boldsymbol{P Q} ) are drawn. Prove that ( boldsymbol{X} boldsymbol{Z}^{2}=boldsymbol{P} boldsymbol{Z} times boldsymbol{Z} boldsymbol{Q} ) | 10 |

436 | ( mathrm{BE}=mathrm{DF} ) f the above statement is true then mention answer as 1 , else mention 0 if false | 10 |

437 | In ( triangle A B C, P Q ) is a line segment intersecting ( A B ) at ( P ) and ( A C ) at ( Q ) such that ( mathrm{PQ} | mathrm{BC} ) and ( mathrm{PQ} ) divides ( triangle mathrm{ABC} ) into two parts equal in area. Find ( frac{B P}{A B} ) | 10 |

438 | The altitudes of triangle are 12,15 and 20 units. The largest angle in the triangle is: A ( .75^{circ} ) B. ( 90^{circ} ) ( c cdot 120^{circ} ) D. ( 135^{circ} ) | 10 |

439 | A ( 15 mathrm{m} ) long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall. | 10 |

440 | If ( A B=D E, B C=E F ) and ( A C=D F ) then ( Delta A B C_{-}-_{-} Delta D E F ) ( A cdot cong ) B. ( approx ) ( c cdot t ) D. > | 9 |

441 | Which condition can be used to prove that the given triangles are SAS congruent? ( A . angle B=angle F, overline{A B} cong overline{D F} ) and ( overline{A C} cong overline{D E} ) B. ( angle A=angle F, overline{A B} cong overline{D C} ) and ( overline{A C} cong overline{D E} ) ( mathrm{c} . angle B=angle C, overline{A B} cong overline{D C} ) and ( overline{A C} cong overline{D E} ) D. ( angle B=angle F, overline{A C} cong overline{D C} ) and ( overline{A C} cong overline{D E} ) ( E ) | 10 |

442 | Take two similar shapes. If you slide rotate or flip one of them, does the similarity remain. | 10 |

443 | In a right-angled, triangle the area of the square drawn on the Hypotenuse is ( 289 c m^{2} ) and the area of the square drawn on the Base is ( 225 mathrm{cm}^{2} ) What will be the area of the square drawn on the Height of the triangle in ( c m^{2} ? ) | 10 |

444 | In the figure, ( P Q R S ) is a parallelogram with ( P Q=15 c m ) and ( R Q=10 c m . L ) is a point on ( R P ) such that ( R L: L P=2: ) 3. ( Q L ) produced meets ( R S ) at ( M ) and ( P S ) produced at ( N . ) Find the lengths of ( P N ) and ( boldsymbol{R} boldsymbol{M} ) A. ( P N=15 mathrm{cm} ; R M=10 mathrm{cm} ) B. ( P N=10 mathrm{cm} ; R M=10 mathrm{cm} ) c. ( P N=25 mathrm{cm} ; R M=15 mathrm{cm} ) D. ( P N=25 mathrm{cm} ; R M=10 mathrm{cm} ) | 10 |

445 | Which minimum measurements do you require to check if the given figures are congruent: Two rhombuses | 9 |

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