Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
Let ΔPQR and ΔABC be two similar triangles,
[Corresponding sides of similar triangles are in the same ratio] [1]
And as corresponding angles of similar triangles are equal
∠A = ∠P
∠B = ∠Q
∠C = ∠R
Construction: Draw PM ⏊ QR and AN ⏊ BC
In ΔPQR and ΔABC
∠PMR = ∠ANC [Both 90°]
∠R = ∠C [Shown above]
ΔPQR ~ ΔABC [By Angle-Angle Similarity]
[Corresponding sides of similar triangles are in the same ratio] [2]
Now, we know that
Area of a triangle
Therefore,
[From 2]
[From 1]
[From 1]
Hence, Proved.