Question

Prove that the area of similar triangles have the same ratio as the squares of corresponding medians.

Answer 1

Suppose ΔABC and ΔPQR are similar triangles.

Since ΔABC and ΔPQR are similar, ... (1)

Also, and

Putting these expressions in (1), we get:

... (2)

In ΔABD and ΔPQS:

and

By SAS similarity criteria, we have

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