Q. 64.1( 263 Votes )

Prove that the ra

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)]

And,

[From (iii)]

ΔABD ~ ΔPQS (SAS similarity)

Therefore, it can be said that

.......(iv)

From (i) and (iv), we get

And hence,

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