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