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

#### List of congruence of triangles Questions

Question No | Questions | Class |
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1 | In ( triangle A B C, A D ) is perpendicular bisector of BC (See adjacent figure). Show that ( triangle A B C ) is an isosceles triangle in which ( boldsymbol{A B}=boldsymbol{A C} ) | 7 |

2 | From the given figure it is stated that ( boldsymbol{A B}=boldsymbol{A C} ) State true or false. 4 . True B. False | 7 |

3 | In the figure, the two triangles are congruent. The corresponding parts are marked. We can write ( Delta ) RAT ( equiv ? ) | 7 |

4 | In the given figure, if ( P Q R S ) is a rectangle which one is true? ( mathbf{A} cdot A r Delta(A P S)=A r Delta(Q R B) ) B. ( P A=R B ) ( mathbf{c} cdot A r(P Q S)=A r(Q R S) ) D. All of the above | 7 |

5 | ( A B C D E ) is a regular pentagon. Show that ( triangle A B C cong triangle A E D ) | 7 |

6 | In the given figure, ( overline{P L} perp overline{O B} ) and ( boldsymbol{P M} perp overline{boldsymbol{O} boldsymbol{A}} ) such that ( overline{boldsymbol{P} boldsymbol{L}}=overline{boldsymbol{P} boldsymbol{M}} . ) Is ( triangle P L O cong triangle P M O ? ) Give reasons in support of your answer | 7 |

7 | ( A B C ) is an isosceles triangle with ( A B=A C ) and ( A D ) is one of its altitude A. State the three pairs of equal parts in ( triangle A D B ) and ( triangle A D C ) B. Is ( triangle A D B cong A D C ) ? Why or why not? c. Is ( angle B=angle C ) ? Why or why not? D. Is ( B D=C D ) ? Why or why not? | 7 |

8 | n the given figure, ( boldsymbol{A B}=boldsymbol{A C} ) Then ( A D ) does not bisects angle ( A ) ( A ). True B. False | 7 |

9 | In the figure above, ( A D=A C=C B ) If the value of ( y ) is ( 28^{circ}, ) what is the value of ( x ? ) | 7 |

10 | You want to show that ( Delta A R T cong Delta P E N ) If you have to use SSS criterion, then you need to show RT=? | 7 |

11 | In given figure ( A B ) is a line-segment. ( P ) and ( Q ) are points on either side of ( A B ) such that each of them is equidistant from the points ( A ) and ( B . ) Show that the line ( P Q ) is the perpendicular bisector of ( A B ) | 7 |

12 | In the figure, ( A B=C D ) and ( angle A= ) ( mathbf{9 0}^{circ}=angle D . ) Then A. ( Delta A B C cong Delta D B C ) by SAS postulate B. ( Delta A B C cong Delta D C B ) by RHS postulate c. ( Delta A B C cong Delta D B C ) by AAS postulate D. ( Delta A B C cong Delta D C B ) by SSS postulate | 7 |

13 | ( triangle A B C ) and ( triangle D B C ) are two iosceles triangle on the same base ( B C ) and vertices ( A ) and ( D ) are on the same sides of ( B C . ) If ( A D ) is exerted to intersect ( B C ) at ( P ), show that ( triangle boldsymbol{A B P} cong ) triangleACP | 7 |

14 | n the following figure, ( boldsymbol{O A}=boldsymbol{O C} ) and ( A B=B C . ) Prove that ( angle A O B=90^{circ} ) ii) ( Delta A O D cong Delta C O D ) iii) ( boldsymbol{A} boldsymbol{D}=boldsymbol{C} boldsymbol{D} ) | 7 |

15 | In the following diagrams, ABCD is a square and APB is an equilateral triangle. n each case, ( Delta A P D cong Delta B P C ) State whether the above statement is true or false. A. True B. False | 7 |

16 | In triangle ( A B C . D ) and ( E ) are points on side ( A B ) such that ( A D=D E=E B ) Through ( D ) and ( E ), lines are drawn parallel to ( B C ) which meet side ( A C ) at points ( boldsymbol{F} ) and ( boldsymbol{G} ) respectively. Through ( boldsymbol{F} ) and ( G ) lines are drawn parallel to ( A B ) which meet side ( B C ) at points ( M ) and ( N ) respectively State whether true or false ( boldsymbol{B} boldsymbol{M}= ) ( M N=N C .(text { Enter } 1 text { if true or } 0 ) otherwise) | 7 |

17 | When two triangles have corresponding sides equal in length, then the two triangles are congruent. A. SAS congruency Theorem B. AA congruency Theorem C. AAA congruency Theorem D. sss congruency Theorem | 7 |

18 | ( ln a Delta A B C, ) BD is the median to the side ( A C, B D ) is produced to ( E ) such that ( B D=D E ) Hence, AE parallel to BC. State whether the above statement is true or false. A. True B. False | 7 |

19 | In the given figure, the point ( P ) bisects ( A B ) and ( D C . ) Prove that ( Delta A P C cong Delta B P D ) | 7 |

20 | Using ASA congruence. What is the ength of ( boldsymbol{P Q} ) ? ( A cdot 9 ) 3. 10 ( c cdot 12 ) D. 14 | 7 |

21 | State true or false: In the given figure, the diagonals ( boldsymbol{A C} ) and ( B D ) intersect at point ( O . ) If ( O B= ) ( O D ) and ( A B / / D C, ) then Area( (triangle D C B)= )Area( (triangle A C B) ) A. True B. False | 7 |

22 | Which of the following can be used to prove that ( Delta A B C cong Delta S R T ? ) ( A cdot A S A ) B. SAS C . RHS D. AAA | 7 |

23 | You want to show that ( Delta mathrm{ART} cong Delta mathrm{PEN} ) If it is given that ( angle mathrm{T}=angle mathrm{N} ) and you are to use SAS criterion, you need to have PN= ? | 7 |

24 | Which congruence criterion do you use in the following? Given ( A C=D F, A B=D E, B C=E F, ) so ( Delta A B C ) ( cong Delta D E F ) | 7 |

25 | A triangle ( A B C ) in which DE ( | B C ), and intersects ( A B ) in ( D ) and ( A C ) in ( E ) Hence, ( frac{A B}{D B}=frac{A C}{E C} ) A. True B. False | 7 |

26 | If a line through one vertex of a triangle divides the opposite sides in the ratio of other two sides, then the line bisects the angle at the vertex. A. True B. False | 7 |

27 | By applying ( S A S ) congruence rule, you want to establish that ( triangle boldsymbol{P} boldsymbol{Q} boldsymbol{R} equiv ) ( triangle F E D . ) It is given that ( P Q=F E ) and ( R P=D E . ) What additional information is needed to establish the congruence? | 7 |

28 | In figure The sides ( B A ) and ( C A ) have been produced such that ( boldsymbol{B A}=boldsymbol{A D} ) and ( C A=A E ) prove that segment ( boldsymbol{D} boldsymbol{E} | boldsymbol{B C} ) | 7 |

29 | In the given figure, ( A B=A C ). Then ( angle B O C=angle A C D ) If the above statement is true then mention answer as 1 . else mention 0 | 7 |

30 | In the given fig. if ( A D=B C ) and ( A D | B C ) then: ( A, A B=A D ) B. AB = DC ( c cdot B C=c D ) D. None | 7 |

31 | AD is an altitude of an isosceles triangle ( A B C ) in which ( A B=A C . ) show that (i) AD bisects BC (ii) AD bisects ( angle A ) | 7 |

32 | na ( Delta A B C ), the sides ( A B, B C ) and ( C A ) are ( mathbf{1 0 c m}, mathbf{8 c m} ) and ( mathbf{7 c m} ) respectively. In AB a point ( P ) is taken such that ( A P=4 c m ). If ( P Q ) is drawn parallel to ( B C ), then its length is equal to A. ( 4.0 mathrm{cm} ) В. ( 3.8 mathrm{cm} ) ( c .3 .5 mathrm{cm} ) ( 0.3 .2 mathrm{cm} ) | 7 |

33 | ( triangle A B C ) is congruent to ( triangle F E D ) ( A ). True 3. Falss | 7 |

34 | ( A B, ) if ( D C=20 mathrm{cm} ) and ( M N=27 mathrm{cm} ) ( 4.43 mathrm{cm} ) 3. 31 ст ( c cdot 34 c m ) ( 30 mathrm{cm} ) | 7 |

35 | For ( Delta A B C ) and ( Delta D E F, A B= ) ( boldsymbol{F} boldsymbol{E}, boldsymbol{B} boldsymbol{C}=boldsymbol{E} boldsymbol{D} ) and ( angle boldsymbol{B}=angle boldsymbol{E} ) Therefore A. ( Delta A B C cong Delta D E F ) B. ( Delta A B C cong Delta E D F ) c. ( Delta B C A cong Delta D E F ) D. ( Delta B C A cong Delta E D F ) | 7 |

36 | In the given figure, ( angle A=angle C E D ). Prove that ( triangle mathrm{CAB} sim triangle mathrm{CED} ). Also, find the value of ( boldsymbol{x} ) | 7 |

37 | If the two sides and the ( _{—-} ) angle of one triangle are respectively equal to two sides and the included angle of the other triangle, then the triangles are congruent. A. Included B. Excluded c. Adjacent D. Any | 7 |

38 | In the given figure, the diagonals ( A C ) and BD intersect at point ( 0 . ) If ( O B=0 D ) and AB//DC, show that: Area ( (Delta D O C)=A r e a(Delta A O B) ) f the ( A(triangle D O C)=21 ) sq. units, then ( boldsymbol{A}(triangle boldsymbol{D} boldsymbol{O} boldsymbol{C})+boldsymbol{A}(triangle boldsymbol{A} boldsymbol{O} boldsymbol{B}) ) is : | 7 |

39 | In the given figure, ( A D=B C, A C= ) BD. Then ( triangle P A B ) is A . equilateral B. right angled ( c . ) scalene D. isosceles | 7 |

40 | In ( triangle P Q R, N ) is a point on ( P R ) such that ( Q N perp P R ) If ( P N times N R=Q N^{2}, ) prove that ( angle P Q R=90^{circ} ) | 7 |

41 | PX bisects angle P. If True enter 1 else if False enter 0 | 7 |

42 | ( X T Q cong Delta X S Q ) | 7 |

43 | n Fig ( , A C=A E, A B=A D ) and ( angle B A D=angle E A C . ) Show that ( B C=D E ) | 7 |

44 | n triangle ( A B C, A B=A C ; B E perp A C ) and ( C F perp A B ) State whether following statement is true or false ( boldsymbol{A F}=boldsymbol{A E} ) A. True 3. False | 7 |

45 | In the quadrilateral ( boldsymbol{A B C D}, boldsymbol{A D}= ) ( C D ) and ( angle A=90^{circ}=angle C . ) Prove that ( boldsymbol{A B}=boldsymbol{B C} ) | 7 |

46 | n ( Delta A B C, angle A B C=90^{circ} ) and ( P ) is a point on ( A C ) such that ( angle P B C= ) ( angle P C B . ) Show that ( : P A=P B . ) Enter 1 if true else 0 | 7 |

47 | ( Delta A B D ) and ( Delta E C D ) are congruent. State whether the above statement is true or false. A . True B. False | 7 |

48 | If the hypotenuse and one of the other two sides of a right angles triangle are equal to the hypotenuse and one of the sides of the other right-angled triangle respectively, then the two right-angled triangles are A. congruent B. unequal c. equilateral D. None of the these | 7 |

49 | n the given figure, it is given that ( boldsymbol{R T}=boldsymbol{T} boldsymbol{S}, angle mathbf{1}=mathbf{2} angle mathbf{2} ) and ( angle mathbf{4}=mathbf{2} angle mathbf{3} ) Prove that ( Delta R B T cong Delta S A T ) | 7 |

50 | In the given figure, ( A B=D C ) and ( B D=C A . ) Prove that ( Delta A B C cong D C B ) | 7 |

51 | Prove that the bisectors of opposite angles of a parallelogram are parallel. | 7 |

52 | Given information is shown marked on the diagrams as shown, To prove that ( A C B ) and DFE are congruent by SAS, what additional information is | 7 |

53 | In a square ( A B C D, ) diagonals meet at 0 Pis a point on BC such that ( O B=B P ). ( angle B O P=3 angle C O P ) State whether the above statement is true or false. A. True B. False | 7 |

54 | In a right angled triangle, prove that the line segment joining the mid-point of the hypotenuse to the opposite vertex is half the hypotenuse. | 7 |

55 | You have to show that ( Delta A M P cong Delta A M Q ) In the following proof, supply the missing reasons steps Reasons (i) PM=QM (i) ( angle mathrm{PMA}=angle mathrm{QMA} ) (i) (ii) AM =AM (iii) (iv) ( Delta mathrm{AMP} cong Delta mathrm{AMQ} ) (iv) | 7 |

56 | In following pairs of triangles, find the pairs which are congruent? Also, write the criterion of congruence | 7 |

57 | In the figure, ( angle A=90^{circ}=angle D ) and ( A B=D C . ) Then ( Delta A B O cong Delta D C O ) by the congruence postulate A . ASA B. SAS ( c . ) sss D. RHS | 7 |

58 | The Indian Navy flight fly in a formation that can be viewed as two triangles with common side. Prove that ( triangle boldsymbol{S} boldsymbol{R} boldsymbol{T} cong ) ( triangle Q R T, ) if ( T ) is the midpoint of ( S Q ) and ( boldsymbol{S} boldsymbol{R}=boldsymbol{R} boldsymbol{Q} ) | 7 |

59 | The bisectors of opposite angles are parallel to each other | 7 |

60 | ( A B C ) is an isosceles triangle in which the altitudes ( B E ) and ( C F ) are drawn to the equal sides ( A C ) and ( A B ) respectively. Then ( mathbf{A} cdot B E=C F ) B. ( B E=A B ) c. ( A B=B C ) D. ( A C=B C ) | 7 |

61 | In a diagram of ( Delta A B C ) and ( Delta D E F ) below, ( boldsymbol{B C} cong boldsymbol{E} boldsymbol{F}, angle boldsymbol{B} cong angle boldsymbol{E} ) and ( angle boldsymbol{A} cong ) ( angle D . ) Which method can be used to prove ( Delta A B C cong Delta D E F ? ) A. AAA congruence B. SAS congruence C. AAS congruence D. SSS congruence | 7 |

62 | In triangle ( A B C, ) the bisector of angle ( B A C ) meets opposite side ( B C ) at point D. If ( B D=C D, ) prove that ( Delta A B C ) is isosceles. | 7 |

63 | In ( triangle A B C ) is on isosceles ( triangle ) with ( A B= ) ( A C ) and ( D ) in a point on BC such that ( A D perp B C . ) Prove that ( angle B A D=angle C A D ) | 7 |

64 | In a right ( triangle A B C, ) right angled at ( C, M ) is the mid point of the hypotenuse of ( A B . C ) is joined to ( M ) produced to a point ( D ) such that ( D M=C M . ) Point ( D ) is joined to point ( boldsymbol{B} ). Then rhis question has multiple correct options A. ( triangle A M C cong triangle B M D ) B. ( angle D B C ) is a right angle c. ( triangle D B C cong triangle A C B ) ( ^{mathrm{D}} cdot C M=frac{1}{2} A B ) | 7 |

65 | ( A P ) bisects angle ( A ) | 7 |

66 | Which of the following condition even if satisfied, does not make the two triangles congruent? A. S.S.S ( side-side-side) B. A.A.A (angle-angle-angle) c. s.A.S (side-angle-side) D. A.S.A (angle-side-angle) | 7 |

67 | ( A B C ) and ( D B C ) are two isosceles triangle on the same side of ( B C . ) Then, ( angle B D A=angle C D A ) A. True B. False | 7 |

68 | ( A D ) is the bisector of BC Which property of triangle applies here? A. ( S A S ) B. ( S S S ) ( c . A A S ) D. none | 7 |

69 | FAC is congruent to GEC. Which statement can NOT be proven?? ( A cdot A F cong G E ) B. ( angle F C A cong angle G C E ) ( c . angle C A F cong angle C D G ) ( . A C cong E C ) ( C ) | 7 |

70 | n right angled 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. Show that: (i) ( triangle A M C cong triangle B M D ) (ii) ( angle D B C ) is a right angle. (iii) ( triangle D B C cong triangle A C B ) ( (mathrm{iv}) C M=frac{1}{2} A B ) | 7 |

71 | The diagonals of a rectangle are unequal in length. A. True B. False | 7 |

72 | If the midpoints of the sides of an equilateral triangle are connected, then they divide it into four triangles all of which are A. congruent B. Similar in shape C. Different D. None of these | 7 |

73 | You want to show that ( Delta mathrm{ART} cong Delta mathrm{PEN} ). If it is given that ( A T=P N ) and you are to use ASA criterion, you need to have? | 7 |

74 | Quadrilateral ( A B C D ) is a square. ( P, Q ) and ( R ) are the points on ( A B, B C ) and ( C D ) respectively, such that ( boldsymbol{A P}= ) ( boldsymbol{B} boldsymbol{Q}=boldsymbol{C} boldsymbol{R} . ) Hence, If ( angle boldsymbol{P} boldsymbol{Q} boldsymbol{R} ) is a right angle, find ( angle P R Q(text { in degrees }) ) | 7 |

75 | Points ( mathrm{M} ) and ( mathrm{N} ) are taken on the diagonal AC of a parallelogram ABCD such that ( A M=C N ) BMDN is a | 7 |

76 | In the given figure, ( 2 A P=5 P B ) and ( 2 C P=5 P D ) Is : ( boldsymbol{A C} | boldsymbol{D B} ) ? If the above statement is true then mention answer as 1 , else mention 0 | 7 |

77 | ( ln Delta A B C, ) D is a point on BC such that ( A B=A D=B D=D C ). then ( angle A D C: angle C=4: 1 ) State whether the above statement is true or false. A. True B. False | 7 |

78 | ( triangle mathrm{ABC} ) and ( triangle ) DEF are two triangles, then to ensure that two triangles ABC and DEF are congruent, 3 conditions ( operatorname{given} ; A B=D E, A C=D F, angle A B C=angle ) DEF are A. sufficient but not necessary B. necessary but not sufficient c. neither necessary nor sufficient D. both necessary and sufficient | 7 |

79 | Two chords ( A B ) and ( A C ) of a circle with centre ( O ) are on the opposite sides of ( boldsymbol{O} boldsymbol{A} . ) Then: A. ( angle O A B=angle O A C ). в. ( angle O A B neq angle O A C ). c. Cannot be determined D. None of the above | 7 |

80 | In a squared sheet, draw two triangles of equal areas such that (i) the triangles are congruent. (ii) the triangles are not congruent What can you say about their perimeters? | 7 |

81 | Complete the following statements: a) Two line segments are congruent if b) Among two congruent angles, one has measure of ( 70^{0} ), the measure of the other angle is c) When we write ( angle A=angle B ), we actually mean.. | 7 |

82 | AB is a line segment ( C ) and ( D ) are points on opposite sides of ( A B ) such that each of them is equidistant from the point ( mathbf{A} ) and ( mathrm{B} ) as in the figure. The line ( mathrm{CD} ) is perpendicular bisector of ( mathrm{AB} ) A. True B. False | 7 |

83 | ABCD is a parallelogram. The sides AB and ( A D ) are produced to ( E ) and ( F ) respectively, such that ( A B=B E ) and ( A D= ) DF. Hence ( Delta B E C cong Delta D C F ) State whether the above statement is true or false. A. True B. False | 7 |

84 | ( A B C D ) is a square and ( Delta P A D ) is equilateral then ( boldsymbol{P B}=mathbf{2 P C} ) A. True B. False | 7 |

85 | If ( mathrm{BC} ) and ( mathrm{AD} ) are equal perpendiculars to line segment ( A B, ) then ( Delta O B C cong ) ( Delta O A D ) by which of the following tests of congruence? What can be said about ( A B ) and ( C D ? ) A. ( A S A ) test, CD bisects AB B. ( S A S ) test, AB bisects ( c ) D c. ( A S A ) test, AB bisects ( c ) D D. ( S A S ) test, CD bisects AB | 7 |

86 | ( triangle A B C ) is an isosceles triangle in which ( A B=A C . ) Show that ( angle B=angle C ) | 7 |

87 | State whether the triangles are congruent or not ( ? ) Give reasons for your answer? | 7 |

88 | t is given that ( A B=B C ) and ( A D= ) EC. The ( triangle A B E cong triangle C B D ) by congruency A. ( S S S ) B. ( A S A ) ( c . S A S ) D. ( A A S ) | 7 |

89 | ( ln Delta A B C ) and ( Delta D E F, A B=D F ) and ( angle A=angle D . ) The two triangles will be congruent by SAS axiom if : A ( . ) BC ( = ) EF B. AC = DE ( c cdot B C=D E ) D. AC = EF | 7 |

90 | the perpendiculars from B and ( mathrm{C} ) to the opposite sides are equal If the above statement is true then | 7 |

91 | If the diagonal BD of a quadrilateral ABCD bisects both ( angle B ) and ( angle D ) then ( A B=A D ) A . True B. False | 7 |

92 | In the given figure, ( A P ) is bisector of ( angle A ) and ( mathrm{CQ} ) is bisector of ( angle C ) of parallelogram ABCD Prove that APCQ is a parallelogram | 7 |

93 | In Fig. 9.20 .0 is the centre of a circle of radius ( 5 mathrm{cm}, ) T is a point such that ( mathrm{OT}= ) ( 13 mathrm{cm} ) and ( mathrm{OT} ) intersects the circle at ( mathrm{E} ). If AB is the tangent to the circle at ( mathrm{E} ) and it intersects the tangents PT and QT at ( A ) and ( B, ) find the length of ( A B ) A ( cdot frac{10}{3} mathrm{cm} ) B. ( frac{20}{3} mathrm{cm} ) ( c .10 mathrm{cm} ) D. ( 15 mathrm{cm} ) | 7 |

94 | In the figure, find the value of ( x ) ( mathbf{A C}=mathbf{C D} ) | 7 |

95 | In given figure ( A B ) is a line segment and line ( l ) is its perpendicular bisector. f a point ( P ) lies on ( l ), show that ( P ) is equidistant from ( A ) and ( B ) | 7 |

96 | If in two triangles ( P Q R ) and ( D E F ) ( boldsymbol{P R}=boldsymbol{E F}, boldsymbol{Q} boldsymbol{R}=boldsymbol{D} boldsymbol{E} ) and ( boldsymbol{P Q}=boldsymbol{F D} ) then ( triangle boldsymbol{P Q R} cong triangle_{—} ) ( mathbf{A} cdot F D E ) в. ( D E F ) c. ( F E D ) D. ( D F E ) | 7 |

97 | and ( m ) are two parallel lines intersected by another pair of paralle lines ( p ) and ( q . ) Then A. ( triangle A B C cong triangle C D A ) B. ( triangle A B C cong triangle A D C ) c. ( triangle A B C cong triangle D C A ) ( triangle A B C cong triangle C A D ) | 7 |

98 | In the given figures, which of the following satisfies A.S.A. condition for congruence? A . Figure I B. Figure I and II C . Figure D. None of these | 7 |

99 | If ( _{-}- ) sides of a triangle are respectively equal to the sides of the other triangle, then the triangles are congruent. A. Three B. Two c. one D. None | 7 |

100 | ( Delta A B C quad ) and ( Delta D B C quad ) are two isosceles triangle on the same base BC and vertices ( A ) and ( D ) are on the same side of BC. if AD is extended to intersect ( mathrm{BC} ) at ( mathrm{p}, ) show that AP is the perpendicular bisector of BC | 7 |

101 | Then Answer: DC produced bisects BC at right angle. If true then enter 1 else if False enter 0 | 7 |

102 | In the given figure, ( triangle D A ) and ( triangle C A B ) are on the same base ( A B ). Prove that ( triangle D A B equiv triangle C A B ) | 7 |

103 | Which condition of congruence will satisfy the diagram? A. SSA B. AAS c. ASA D. sss | 7 |

104 | Which of the following pair of triangles are congruent by RHS criterion? (i) (ii) (iii) (iv) ( A cdot ) (i) and (ii) B. (iii) and (iv) c. (i) and (iii) D. (ii) and (iv) | 7 |

105 | If in two triangles ( Delta A B C ) and ( Delta P Q R ) ( A B=Q R, B C=P R ) and ( C A=P Q ) then : A. ( Delta A B C cong Delta P Q R ) в. ( Delta C B A cong Delta P R Q ) c. ( Delta B A C cong Delta R P Q ) D. ( Delta P Q R cong Delta B C A ) | 7 |

106 | Prove that the line segment joining the mid point of the diagonals of a trapezium is parallel to each of the parallel sides and is equal to half the difference of these sides? | 7 |

107 | In ( Delta A B C, A B=A C ) and ( A D ) is perpendicular bisector of ( boldsymbol{B C} ). The property by which ( Delta A D B ) is not congruent to ( Delta A D C ) is A. SAS property B. SSS property c. RHS property D. AAA property | 7 |

108 | In the figure given below, ( D E | B C ). If ( boldsymbol{A D}=boldsymbol{p} mathrm{cm}, boldsymbol{D B}=boldsymbol{p}-boldsymbol{2} mathrm{cm}, boldsymbol{A} boldsymbol{E}= ) ( p-1 mathrm{cm}, ) then find the value of ( mathrm{p} ) ( A ) B. c. None ( D ) | 7 |

109 | ( boldsymbol{O} boldsymbol{E}=frac{1}{2} boldsymbol{A} boldsymbol{B} ) | 7 |

110 | Which congruence criterion do you use in the following? Given: ( angle mathrm{MLN}=angle mathrm{FGH}, angle mathrm{NML}=angle mathrm{HFG}, mathrm{ML} ) = FG. So ( Delta ) LMN ( equiv Delta G F H ) | 7 |

111 | On the sides ( A B ) and ( A C ) of triangle ( A B C ), equailateral triangle ( A B D ) and ( A C E ) are drawn, then ( angle C A D=angle B A E ) If true then enter 1 and if false then enter 0 | 7 |

112 | ABCD is a square ( P, Q ) and ( R ) are the points on ( A B, B C ) and ( C D ) respectively; such that ( A P=B Q=C R ) Hence, ( P B=Q C ) If the above statement is true then mention answer as 1 , else mention 0 if false | 7 |

113 | ( frac{B D}{B E}=frac{C D}{C E} ) A. True B. False | 7 |

114 | In the parallelogram ABCD, the angles A and ( C ) are obtuse. Points ( X ) and ( Y ) are taken on the diagonal BD such that the angles ( mathrm{XAD} ) and ( mathrm{YCB} ) are right angles. Prove that: ( X A=Y C ). State whether the above statement is true or false. A. True B. False | 7 |

115 | Which congruence criterion do you use in the following? Given: ( mathrm{EB}=mathrm{BD}, mathrm{AE}=mathrm{CB}, angle mathrm{A}=angle mathrm{C}=90^{circ} ) So ( Delta A B E equiv Delta C D B ) | 7 |

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