posted by karan .
ABC is a triangle BD & CE are altitudes drawn from the vertex B & C. Prove that ABC is an isoceles triangle
So far, ABC is just any triangle. The addition of the altitudes do not help.
If it is further specified that BD intersects the segment AC at D, and CE intersects segment AB at E, and that BD and CE are equal, then it is possible to prove that triangles EBC and DCB are congruent.
(Use Pythagoras to prove that the third sides are equal, and use SSS for congruence).