In the adjacent figure. (i) Are ΔABC and ΔDCB congruent? (ii) Are

1.	In the adjacent figure. (i) Are ΔABC and ΔDCB congruent? (ii) Are ΔAOB congruent to ΔDOC’? Also identify the relation between corresponding elements and give reason for your answer.
Answer» i) yes. ∠ACB = ∠DBC BC = BC ∠ABC = ∠DCB (by angle sum property) ∴ ΔABC ≅ ΔDCB (A.S.A) ii) yes ∠A = ∠D ∠ABO = ∠DCO (angle sum property) AB = DC [From (i)] ∴ ΔAOB ≅ ΔDOC (A.S.A) Otherwise ΔAOB and ΔDOC are similar by A.A.A. In congruent triangles corresponding parts are equal.

In the adjacent figure. (i) Are ΔABC and ΔDCB congruent? (ii) Are ΔAOB congruent to ΔDOC’? Also identify the relation between corresponding elements and give reason for your answer.

Answer»

i) yes.

∠ACB = ∠DBC

BC = BC

∠ABC = ∠DCB (by angle sum property)

∴ ΔABC ≅ ΔDCB (A.S.A)

ii) yes

∠A = ∠D

∠ABO = ∠DCO (angle sum property)

AB = DC [From (i)]

∴ ΔAOB ≅ ΔDOC (A.S.A)

Otherwise ΔAOB and ΔDOC are similar by A.A.A. In congruent triangles corresponding parts are equal.