# CM and RN are respectively the medians of triangle ABC and triangle PQR. if ABC ~PQR, prove that : AMC~ PNR CM / RN =AB/PQ CMB ~ RNQ

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we know that ΔABC≈ ΔPQR

AB/PQ = BC/QR = AC/PR ------------------------(1)

fromΔAMC and ΔPNR

∠A = ∠P

∠M = ∠N = 90

AC = PR

by ASA similarity

ΔAMC ≈ΔPNR ----PROVED

from this

AC/PR = CM/RN = AM/PN

FROM ------(1)

AB/PQ = BC/QR = AC/PR

from that

CM/RN = AB/PQ -----PROVED

from ΔBMC and ΔQNR

∠B = ∠Q

∠M = ∠N = 90

BC = RQ

by ASA similarity

ΔBMC≈ΔQNR ------PROVED