Question

4. If the altitudes from two vertices of a triangle two opposite sides are equal, prove that triangle is

isosceles.

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Answer 1

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Answer 2

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△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