Q33 of 40 Page 1

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


Let us assume two similar triangles as ΔABC ∼ ΔPQR.


Let AD and PS be the medians of these triangles


Then, because ΔABC ∼ΔPQR


…(i)


∠A = ∠P, ∠B = ∠Q, ∠C = ∠R …(ii)


Since AD and PS are medians,


BD = DC = BC/2


And, QS = SR = QR/2


Equation (i) becomes,


…(iii)


In ΔABD and ΔPQS,


∠B = ∠Q [From (ii)]


[From (iii)]


ΔABD ∼ ΔPQS (SAS similarity)


Therefore, it can be said that




From (i) and (iv), we get



and hence,



Hence, proved!


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