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A B C is a triangle is which B E and C F...

`A B C` is a triangle is which `B E` and `C F` are, respectively, the perpendiculars to the sides `A C` and `A B` . If `B E=C F` , prove that ` A B C` is isosceles.

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In order to prove that the `triangleABC` is isosceles, we will prove that `/_B=/_C`.
To prove this, we will prove that `/_\BFC~=/_\CEB`.
In these two triangles, we have `BE=CF` [Given]
`BC=BC` [common]
So, by RHS congruence criterion, we obtain `/_\BFC~=/_\CEB`
`=>/_FBC=/_ECB`
`=>/_ABC=/_ACB`
`=>AB=AC` [since Sides opposite to equal angles are equal]
So, `/_\ABC` is isosceles.
Hence Proved.
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