If D and E are points on sides AB and AC respectively of a Δ ABC su – InterviewSolution

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1.

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

Answer»

We have DE∥BC

by the converse of proportionality theorem

AD/DB=AE/EC

AD/DB=AE/DB [BD=CE]

AD=AE

Adding D both sides

AD+BD=AE+DB

AD+BD=AE+EC [BD=CE]

AB=AC

⊿ABC is isosceles

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