Answer :

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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