Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

Let us assume ΔABC & ΔPQR are similar

Area of ΔABC = 0.5 ×AD ×BC

Area of ΔPQR = 0.5 ×PS ×QR

Now since the two triangles are similar so the length of sides and perpendiculars will also be in proportion

…Equation 1

…Equation 2

From Equation 1 We get

Putting in Equation 2 we get

⇒

So we can see ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides

Hence Proved