Q5 of 42 Page 214

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

Need to prove that the ratio of area of two similar triangles is equal to the square of the ratio of their corresponding medians


⇒ In case of two similar triangles ABC and PQR we have


⇒


=


⇒ Let us assume AD and PM are the medians of these two triangles


Then


⇒ = =


Hence, ar(Δ ABC) : ar(Δ PQR) = AD2 : PM2


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