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: Let us assume two similar triangles as ΔABC ΔPQR. Let AD and PS be the medians of these triangles
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,
In ΔABD and ΔPQS,
∠B = ∠Q [From (ii)]
And,
AB/PQ=BD/QS [From (iii)]
ΔABD ΔPQS (SAS similarity)
Therefore, it can be said that
From (i) and (iv), we get
And hence,
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