Q2 of 56 Page 6

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

Given BD = CE


To Prove: ∆ ABC is isosceles


Theorem Used:


Converse of Basic Proportionality theorem:


If a line divides any two sides of triangle in the same ratio, then the line must be parallel to third side.


Proof:



We have DE∥BC


By the converse of proportionality theorem,



As BD = CE



AD = AE


Adding BD both sides,


AD+BD=AE+DB


As BD = CE


AD+BD=AE+EC


AB = AC


∆ABC is isosceles.


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