Question

□ABCD is parallelogram point E is on side BC .line DE intersects ray AB in T . Prove that DE×BE=CE×TE.

Answer 1

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Answer 2

Given that,

ABCD is a parallelogram.

We need to prove that $DE\times BE=CE\times TE$

Using diagram

In ΔBET and ΔCED

For vertically opposite angles,

$\angle BET=\angle CED$

For alternate angles,

AT and CD is parallel lines and DT is a transversal line

By AA test of similarity,

$\triangle BET\approx \triangle CED$

We know that,

Corresponding sides are proportional.

So, $\dfrac{BE}{CE}=\dfrac{ET}{ED}$

$BE\times ED=CE\times ET$

Hence, This is proved.