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,

`"AD"/"DE"="AE"/"EC"`

`rArr"AD"/"DB"="AE"/"DB"`      [∵BD = CE]

⇒ AD = AE

Adding DB on both sides

⇒ AD + DB = AE + DB

⇒ AD + DB = AE + EC [∴ BD = CE]

⇒ AB = AC

⇒ Δ ABC is isosceles