Question

In the given figure, the sides BA and CA have been produced such that BA = AD and CA = AE. Prove that segment DE || BC.

Answer 1

It is given that

We have to prove that

Now considering the two triangles we have

In

(Given)

(Given)

We need to show to prove.

Now

(Vertically opposite angle)

So by congruence criterion we have

So and

Then

, and

Hence from above conditions .