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

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