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prove that The areas of the two similar ...

prove that The areas of the two similar triangles are in the ratio of the square of the corresponding medians.

Text Solution

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BD=DC=1/2BC
QS=SR=1/2QR
`(BD)/(QS)=(DC)/(SR)=(BC)/(QR)`
-(1) `/_ABC`~`/_PQR`(AAA)
`(AB)/(PQ)=(BC)/(QR)=(CA)/(RP)`
`angleB=angleQ`
`/_ABC`~`/_PQS`
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