Question

Prove that Triangles having equal areas and having one side of one of the triangle equal to one side of the other have their corresponding altitudes equal.

Answer 1

Given:

Two triangles ABC and DEF are such that

(i) ar (ΔABC) = ar (ΔDEF)

(ii) BC = EF

AM and DN are altitudes of triangle ABC and triangle DEF respectively.

To prove:

AM = DN

Proof:

In triangle ABC, AM is the altitude, BC is the base.

Hence the theorem is proved.