Q23 of 46 Page 1

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

Given: Δ ABC ~ Δ PQR


To Prove:


Construction: Draw AM ⊥ BC, PN ⊥ QR



We know that,




…(i)


In Δ ABM and Δ PQN,


∠B = ∠Q


(Given: Δ ABC ~ Δ PQR & angles of similar triangles are equal)


∠M = ∠N (each 90°)


So, Δ ABM ~ Δ PQN (AA similarity criterion)


…(ii)


(Δ ABC ~ Δ PQR) …(iii)


Hence, from (i)



[From (ii) and (iii)]



Using (iii)



Hence Proved


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