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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.
Solution
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
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