In the adjoining figure, ∠ABC = ∠ACB, D and E are points on the sides AC and AB respectively such that BE = CD. Prove that

(i) △EBC ≅ △DCB

(ii) △OEB ≅ △ODC

(iii) OB = OC.

(i) Given, ∠ABC = ∠ACB.

∴ ∠EBC = ∠DCB.

In △EBC and △DCB,

∠EBC = ∠DCB (Proved)

BE = CD (Given)

BC = BC (Common)

Hence, proved △EBC ≅ △DCB by SAS axiom.

(ii) We know that, △EBC ≅ △DCB.

Subtracting common △OBC from both sides we get,

⇒ △EBC - △OBC ≅ △DCB - △OBC

⇒ △OEB ≅ △ODC

Hence, proved that △OEB ≅ △ODC.

(iii) We know that,

△OEB ≅ △ODC

We know that corresponding angles of congruent triangles are equal.

∴ OB = OC.

Hence, proved that OB = OC.