Choose the correct statement.
(a) In two triangles, ABC and PQR, ∠A = 30°, ∠B = 70°, ∠P = 70°, ∠Q = 80°
and AB = RP, then
(i) ΔABC ≌ ΔPQR (ii) ΔABC ≌ ΔQRP
(iii) ΔABC ≌ ΔRPQ (iv) ΔABC ≌ ΔRQP
(b) In two triangles ABC and DEF, AB = DE, BC = DF and AC = EF, then
(i) ΔABC ≌ ΔDEF (ii) ΔABC ≌Δ ΔEFD
(iii) ΔABC ≌ ΔFDE (iv) None of these
(c) In the given figure, the congruency rule used in proving ΔACD ≌ ΔADB is
(i) ASA (ii) SAS
(iii) AAS (iv) RHS
(d) In a triangle PQR if ∠QPR = 80° and PQ = PR, then ∠R and ∠Q are
(i) 80°, 70° (ii) 80°, 80°
(iii) 70°, 80° (iv) 50°, 50°
(e) In the given figure, find the length of PM.
(i) 3 cm (ii) 5 cm
(iii) 4 cm (iv) 2 cm
2. ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA.
Prove that ΔABD ≌ ΔBAC.
3. In the given figure, triangles PQC and PRC are such that QC = PR and PQ = CR.
Prove that ∠PCQ = ∠CPR.
4. In the given figure, AB = AD, AC = AE and ∠BAD = ∠EAC, then prove that BC = DE.
5. ABC is isosceles triangle in which AC= BC. AD and BE are respectively two attitudes to side
BC and AC. Prove that AE = BD.
6. In the given figure, AD is bisector of ∠BAC and ∠CPD = ∠BPD.
Prove that ΔCAP ≌ ΔBAP.
7. ΔPQR is given and the sides QP and RP have been produced to S and T such that PQ = PS
and PR = PT. Prove that the segment QR || ST.
8. In the given figure, equilateral ΔABD and ΔACE are drawn on the sides of a ΔABC.
Prove that CD = BE.
9. ABCD is a parallelogram. If the two diagonals are equal, find the measure of ∠ABC.
10. In ΔABC and ΔADC, AB = AD and BC = CD. Prove that ∠ABC ≌ ΔADC.
11. Prove that angles opposite to equal sides of an isosceles triangle are equal.
ANSWER KEY
1. (a) (iii) (b) (iv) (c) (ii) (d) (iv) (e) (iii)
2. Proving
3. Proving
4. Proving
5. Proving
6. Proving
7. Proving
8. Proving
9. 90°
10. Proving
11. Proving.
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