Question

Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.

Answer 1

Lines AB and CD Intersect at O

Such that BC ∥ AD and 

BC = AD …….(i)

To prove : AB and CD bisect at O.

First we have to prove that Δ AOD ≅ Δ BOC 

∠OCB =∠ODA [AD||BC and CD is transversal] 

AD = BC [from (i)] 

∠OBC = ∠OAD [AD||BC and AB is transversal] 

By ASA Criterion: 

Δ AOD ≅ Δ BOC 

OA = OB and OD = OC (By c.p.c.t.) 

Therefore, AB and CD bisect each other at O. 

Hence Proved.