5. Example problems V

In the given figure, \(CM\) and \(RN\) are respectively the medians of \(\Delta ABC\) and \(\Delta PQR\). If \(\Delta ABC \sim \Delta PQR\), prove that:

 

(i) \(\Delta AMC \sim \Delta PNR\)

 

(ii) \(\frac{CM}{RN} = \frac{AB}{PQ}\)

 

(iii) \(\Delta CMB \sim \Delta RNQ\)