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ORIf AD and PM are medians of triangles ABC and PQR respectively where Δ ABC~ Δ PQR,AB ADprove that pPQ PM |
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Answer» It is given that ΔABC ~ ΔPQRWe know that the corresponding sides of similar triangles are in proportion.∴ AB/PQ = AC/PR = BC/QR ...(i)Also, ∠A = ∠P, ∠B = ∠Q, ∠C = ∠R …(ii)Since AD and PM are medians, they will divide their opposite sides.∴ BD = BC/2 and QM = QR/2 ...(iii)From equations(i)and(iii), we getAB/PQ = BD/QM ...(iv)In ΔABD and ΔPQM,∠B = ∠Q [Using equation(ii)]AB/PQ = BD/QM [Using equation(iv)]∴ ΔABD ~ ΔPQM (By SAS similarity criterion)⇒ AB/PQ = BD/QM = AD/PM hit like if you find it useful |
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