Prove that the areas of similar triangles have the same ratio as the squares of corresponding altitudes.

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Solution

Suppose ΔABC and ΔPQR are similar triangles.

Let p₁ and p₂ be the lengths of the corresponding altitudes of ΔABC and ΔPQR respectively.

Hence, the ratio of the areas of similar triangles is equal to the ratio of the squares of their corresponding altitudes.

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