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TRIANGLES
1. If the corresponding angles of two triangles are equal, then they are always congruent is
a. True b. False c. cannot be determined d. None of these
2. Which of the following is not a congruence of triangle
a. SSA b. SAS c. ASA d. SSS
3.
𝐼𝑓 ∆ 𝐴𝐵𝐶 ⩭ ∆ 𝑃𝑄𝑅 𝑡ℎ𝑒𝑛 𝑤ℎ𝑖𝑐ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑖𝑠 𝑛𝑜𝑡 𝑡𝑟𝑢𝑒
a. BC=PQ b. AC=PR c. BC=QR d. AB=PQ
4. If AB=QR, BC=RP and CA = PQ then which of the following holds
a. b. c. d. None of these.
∆ 𝐴𝐵𝐶 ⩭ ∆ 𝑃𝑄𝑅 ∆ 𝐶𝐵𝐴 ⩭ ∆ 𝑃𝑄𝑅 ∆ 𝐶𝐴𝐵 ⩭ ∆ 𝑃𝑄𝑅
5. In triangles ABC and DEF, AB=FD and ∠A=∠D. The two triangles will be congruent by
SAS axiom if
a. BC=EF b. AC=DE c. AC=EF d. BC=DE
6. If AB = QR, BC = PR and CA = PQ, then
a. b. c. d.
∆ 𝑃𝑄𝑅 ⩭ ∆ 𝐵𝐶𝐴 ∆ 𝐵𝐴𝐶 ⩭ ∆ 𝑅𝑃𝑄 ∆ 𝐶𝐵𝐴 ⩭ ∆ 𝑃𝑅𝑄 ∆ 𝐴𝐵𝐶 ⩭ ∆ 𝑃𝑄𝑅
7. Which of the is not a criteria for congruence of triangles:-
a. SSA b. SAS c. ASA d. SSS
8. In triangle ABC ⩭ PQR and RPQ is not congruent of ABC, then which of the
∆ ∆ ∆
following is not true?
a. BC=PQ b. AC=PR c. BC=QR d. AB=PQ
9. then which of the following is not true
∆ 𝐴𝐵𝐶 ⩭ ∆ 𝑃𝑄𝑅
a. BC=PQ b. AC=PR c. BC=QR d. AB=PQ
10. If AB = QR, BC=RP and CA=PQ then which of the following holds
a. b. c. d. None of
∆ 𝐴𝐵𝐶 ⩭ ∆ 𝑃𝑄𝑅 ∆ 𝐶𝐵𝐴 ⩭ ∆ 𝑃𝑄𝑅 ∆ 𝐶𝐴𝐵 ⩭ ∆ 𝑃𝑄𝑅
these
11. D,E and F are mid points of the sides BC, CA and AB respectively of ABC. Then DEF
∆ ∆
is congruent to triangle :-
a. ABC b. AEF c. BFD,CDE d. AFE,BFD,CDE
12. AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.
13. In the right triangle ABC, right angled at C, M is the midpoint of hypotenuse AB. C is
joined to M and produced to a point D such that DM = CM. Point D is joined to point B.
Show that:
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a.
∆ 𝐴𝑀𝐶 ⩭ ∆ 𝐵𝑀𝐷
b. DBC is a right angle.
∠
c.
∆ 𝐷𝐵𝐶 ⩭ ∆ 𝐴𝐶𝐵
d.
𝐶𝑀 =
1
2
𝐴𝐵
14. In Fig, AC = AE, AB = AD and ∠ BAD = ∠ EAC. Show that BC = DE.
15. Write ASA congruence rule of triangle and prove it.
16. ABCD is a quadrilateral in which AD=BC and ∠DAB=∠CBA, prove that
a. b. BD=AC c. ∠ABD = ∠BAC
∆ 𝐴𝐵𝐷 ⩭ ∆ 𝐵𝐴𝐶
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17. AD is an altitude of an isosceles triangle ABC in which AB = AC, show that :
a. AD bisects BC
b. AD bisects ∠A
18. Prove that if two lines intersect then vertically opposite angles are equal.
19. In a park, there are two triangular flowers bed. Flowers bed ABC has two sides AD = 8
cm, BC = 6 cm, and CA = 10 cm. Flower bed PQR has two sides PQ = 8cm, QR = 10
cm and RP = 6 cm.
a. Using the given information, can we conclude that flower bed ABC is congruent
to flower bed PQR? Why or why not?
b. If ∠A = 40
0
and ∠B = 60
0
in flower bed ABC, what is the measure of ∠C?
20. In an isosceles triangle ABC, with AB = AC, the bisectors of ∠ B and ∠ C intersect each
other at O. Join A to O. Show that :
a. OB=OC
b. AO bisects ∠A
21. In fig, E and F are respectively the mid-points of equal sides AB and AC of ∆ ABC .
Show that BF = CE.
22. AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that:
a. AD bisects BC
b. AD bisects ∠A
23. Write ASA congruence rule of triangle and prove it.
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24. Two sides AB and BC and median AM of one triangle ABC are respectively equal to
sides PQ and QR and median PN of ∆ PQR . Show that:
a. b.
∆ 𝐴𝐵𝑀 ⩭ ∆ 𝑃𝑄𝑁 ∆ 𝐴𝐵𝐶 ⩭ ∆ 𝑃𝑄𝑅
25. A ladder manufacturing company manufactures foldable step ladders of aluminium as
shown in the figure. The lengths of two legs AB and AC are equal to 110 cm and the
angle between the two legs is 30
0
. On the basis of the above information answer the
following questions:
a. Find the value of ∠ABC
b. If ∠BAC = 60
0
, then find the length of BC
c. What type of triangle is ABC
d. If two triangle ABC and DEF, if ∠A = ∠D, AB = DE and AC = DF then write the
name of criterion by which you triangles are congruent?
26. ABC is an isosceles triangle with AB = AC, AP BC then show that ∠B = ∠C
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