Q. 6 4.1( 181 Votes )

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

Answer :

Let us assume two similar triangles as ΔABC ~ ΔPQR.

Let AD and PS be the medians of these triangles

Then, because ΔABC ~ΔPQR


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,



B = Q [From (ii)]


[From (iii)]

ΔABD ~ ΔPQS (SAS similarity)

Therefore, it can be said that


From (i) and (iv), we get

And hence,

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