Question

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

Answer 1

We have, DE || BC
Therefore, by BPT, we have,

Adding DB on both sides
⇒ AD + DB = AE + DB
⇒ AD + DB = AE + EC    [∴ BD = CE]
⇒ AB = AC
⇒ Δ ABC is isosceles