Question

In the given figure, CM and RN are respectively the medians of ΔABC and ΔPQR. If ΔABC ∼ ΔPQR, then prove that ΔAMC ∼ ΔPNR.

Answer 1

Given: ΔABC ∼ ΔPQR

and CM and RN are medians of ΔABC and ΔPQR respectively.

To Prove: ΔAMC ∼ ΔPNR

Proof: ΔABC ∼ ΔPQR   ...(Given)

∴ ∠A = ∠P,

and `(AB)/(PQ) = (BC)/(QR) = (AC)/(PR)`

`(AB)/(PQ) = (AC)/(PR)`

`(2AM)/(2PN) = (AC)/(PR)`

`(AM)/(PN) = (AC)/(PR)`

and ∠A = ∠P

∴ ΔAMC ∼ ΔPQR  ...(SAS Test)

Hence Proved.