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

It is given that

BC = AD   

 BC || AD

We have to prove that AB and CD bisect at O.

If we prove that ΔAOD ≅ ΔBOC , then

We can prove AB and  CDbisects atO.

Now in  ΔAOD and ΔBOC

AD = BC(Given)

∠OBC =∠OAD (Since AD || BC and AB is transversal)

And ∠OCB = ∠ODA(since AD || BC and CD is transversal)

So by ASAcongruence criterion we have,

ΔAOD ≅ ΔBOC, so

OA = OB

OD = OC

Hence ABand  CD bisect each other at O.