Question

In the given figure, prove that:
i) AOD ~= BOC
ii) AD= BC
iii) ADB =ACB​

Answer 1

Answer:

Proof:

In △ AOD and △ BOC

OA = OB (given)

∠AOD = ∠BOC (vertically opposite angles)

OD = OC (given)

(i) ∴ △ AOD ≅ △BOC (S.A.S. Axiom)

Hence (ii) AD = BC (c.p.c.t.)

and (iii) ∠ADB = ∠ACB (c.p.c.t.)

(iv) △ADB ≅ △BCA

△ADB = △BCA (Given)

AB = AB (Common)

△AOB ≅ △BCA

Hence proved.