# In the given figure, CM and RN are respectively the medians of ΔABC and ΔPQR. If ΔABC ~ ΔPQR, prove that:(i) ΔAMC ~ ΔPNR(ii) (iii) ΔCMB ~ ΔRNQ Given: CM is the median of ABC and RN is the median of PQR

Also, ABC ~ PQR

To Prove: (i) AMC ~ PNR

CM is median of ABC

So, …(1)

Similarly, RN is the median of PQR

So, …(2)

Given ABC ~ PQR (corresponding sides of similar triangle are proportional)  (from (1) and (2)) …(3)

Also, since ABC ~ PQR

A = P …(4)

(corresponding angles of similar triangles are equal)

In AMC and PNR

A = P (from (4)) (from (3)) AMC ~ PNR (by SAS similarity)

Hence Proved

(ii)To Prove: In part (i), we proved that AMC ~ PNR

So, (corresponding sides of a similar triangle are proportional)

Therefore,   Hence Proved

(iii) CMB ~ RNQ

Given ABC ~ PQR (corresponding sides of similar triangle are proportional)  (from (1) and (2)) …(5)

Also, since ABC ~ PQR

B = Q …(6)

(corresponding angles of similar triangles are equal)

In CMB and RNQ

B = Q (from (6)) (from (5)) CMB ~ RNQ (by SAS similarity)

Hence Proved

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