`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.

Explanation

"Given that ABC is a triangle in which BE and CF are perpendiculars to the sides AC and AB respectively such that BE=CF.
We have to prove that `triangle ABC` is an isosceles.
Now consider `triangle BCF and triangle CBE `, We have
`angle BCF = angle CEB = 90^@` ( given )
`BC=CB` (common sides )
`CF=BE` ( given )
`therefore triangle BFC= triangle CEB`
`angle FBC = angle ECB`
`angle ABC = angle ACB`
`AB = AC ` [ sides opposite to equal angles are equal ]
`therefore triangle ABC` is an isosceles .
"