Question

In ∆ABC, the altitudes from vertex B and C intersect at point M, so that BM = CM. Prove that ∆ABC is isosceles.

Answer 1

BCM is isosceles. Due to the fact that BM=CM

An altitude in the third vertex A of the triangle ABC, has to go through M, and it will intersect BC in the middle.

This means that the angles <CBA = <BCA, implies that ABC is isosceles.