Question extracted from RD sharma of class 10th, Chapter no. 4

Chapter name:- Triangles

Exercise :- 4.2

This is very basic and important questions. And has been asked in several times in exams.

In this question we have been given that D and E are the points on sides AB and AC respectively of a ΔABC

such that DE ∥ BC and BD = CE.

Now we have to Prove that ΔABC is isosceles.

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RD sharma, DHANPAT RAI publication

In Δ ABC, DE ∥ BC and BD = CE.

To prove: that Δ ABC is isosceles.According to Thales Theorem,

AD/DB = AE/EC

But BD = CE (Given)

Therefore, we get,AD = AE

Now, BD = CE and AD = AE.

So, AD + BD = AE + CE.

Therefore, AB = AC.

Therefore, ΔABC is isosceles.Hence proved