In the given figure, CM and RN are respectively the medians of Δ ABC and Δ PQR. If ABC ∼ PQR, then prove that: (i) AMC ∼ PNR (ii) CMB ∼ RNQ ()

(i) \(\displaystyle \triangle \mathrm{ABC} \sim \triangle \mathrm{PQR} \Rightarrow \angle \mathrm{A}=\angle \mathrm{P}\) \(\displaystyle \frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{\mathrm{AC}}{\mathrm{PR}} \Rightarrow \frac{2 \mathrm{AM}}{2 \mathrm{PN}}=\frac{\mathrm{AC}}{\mathrm{PR}}\) (as CM and RN are the medians) \(\displaystyle \therefore \triangle \mathrm{AMC} \sim \triangle \mathrm{PNR}\)