If D and E are points on sides AB and AC respectively of a ∆ABC such that DE || BC and BD = CE. Prove that ∆ABC is isosceles.

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Solution

It is given that in , DE || BC and BD = CE.

We have to prove that ∆ABC is isosceles.

By Thales theorem we have

Now and

So

Hence

So, ∆ABC is isosceles

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