In ∆abc, the altitudes from vertex b and c intersect at point m, so that bm = cm. prove that ∆abc is isosceles.

BM=CM implies that BCM is isosceles. This means that an altitude from the third vertex A of the triangle ABC, which must necessarily go through M will intersect BC exactly in the middle. This implies that the angles <CBA = <BCA which means the ABC is isosceles.

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