Question

if the altitude for two vertices of a triangle to the opposite sides are equal, prove that the triangle is isosceles.

Answer 1

∆ABC is an isosceles tangent as two sides are equal to each other.

In △ABE and △ACF

∠AEB=∠AFC (90⁰ each)

∠BAE=∠CAF (common angle)

∠ABE=∠ACF using angle sum property

BE=CF

⇒ △ABE≅△ACF

⇒ AB=AC

∴ △ABC is an isosceles tangent as two sides are equal to each other