Question

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. Use the above theorem for the following:If the areas of two similar triangles are equal, prove that they are congruent.

Answer 1

Given: Two triangles ABC and PQR such that ΔABC ~ ΔPQR

Construction: Draw AM ⊥ BC and PN ⊥ QR.

Now, in ΔABM and ΔPQN,

Now, let DABC ~ DPQR such that