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18 In the adjoining figure, CM and RN 'arerespectively the medians of ΔABC and ΔΙ'QR.If Δ/ABC ~ ΔΙΟ, prove that:CM ABRN PO(iii) aCMB ~ ΔRNQ. |
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Answer» From the above the diagrams CM and RNare the medians for the triangles. we know thatΔABC≈ΔPQR AB/PQ = BC/QR = AC/PR ------------------------(1)fromΔAMC andΔPNR∠A =∠P∠M =∠N = 90AC = PRby ASA similarityΔAMC≈ΔPNR ----PROVEDfrom thisAC/PR = CM/RN = AM/PNFROM ------(1)AB/PQ = BC/QR = AC/PRfrom thatCM/RN = AB/PQ -----PROVEDfromΔBMC andΔQNR∠B =∠Q∠M =∠N = 90BC = RQby ASA similarityΔBMC≈ΔQNR ------PROVED |
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