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Question

If D and E are points on sides AB and AC respectively of ΔABC such that DE || BC and BD = CE. Prove that ΔABC is isoscles.

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Solution

If DEBC
From the fig.
ADBD=AECE (by Basic Proportionality Theorem)
Adding 1 on both sides
ADBD+1=AECE+1
(AD+BD)BD=(AE+CE)CE
ABBD=ACCE
As from the given data,
BD=CE
so,
ABBD=ACBD
AB=AC
As two sides of the triangle are equal
ABC is an issosceles triangle.


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