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In the given figure, (AD)/(DB)=(AE)/(EC...

In the given figure, `(AD)/(DB)=(AE)/(EC)` and `angle ADE=angle ACB`. Prove that `Delta ABC` is an isosceles triangle.

Text Solution

Verified by Experts

We have,
`(AD)/(DB)=(AE)/(EC)rArr DE||BC` [ by the convrse of Thale's theorem]
`:. angle ADE= angleABC` (crossponding `angle`).
But, `angle ADE= angleACB` (give) .
`:. angle ABC=angle ACB`.
So, AB=AC [ sides opposite to equal angles.]
Hence, `Delta ABC` is an isosceles triangle.
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