Question

If the points d and E are situated on the sides AB and AC respectively in a triangle ABC. Such that BD =CE, then prove that ABC is an isosceles triangle​

Answer 1

Given :

∆ABC in which D and E are points on sides AB and AC respectively, such that BD = CE.

To prove : DE || BC.

Proof:

In ∆ABC, we have

∠B = ∠C

⇒ AC = AB

⇒ AB = AC

[Sides opposite equal angles arc equal]

⇒ AD + DB = AE + EC

But BD = CE

⇒ AD = AE

Thus, we have

AD = AE and BD = CE

=> AD/BD = AE/BE

Therefore, by converse of Basic proportionality theorem, we get DE || BC.

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