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Question
In ΔPQR, MN is parallel to QR and `(PM)/(MQ) = 2/3`
1) Find `(MN)/(QR)`
2) Prove that ΔOMN and ΔORQ are similar.
3) Find, Area of ΔOMN : Area of ΔORQ
Solution
In ΔPMN and ΔPQR, MN || QR
`=> angle PMN =anglePQR` (alternate angles)
`=> angle PNM = anglePRQ` (alternate angles)
=> ΔPMN ~ ΔPQR (AA postulate)
`= (PM)/(PQ) = (MN)/(QR)`
`=> 2/5 = (MN)/(QR) [(PM)/(MQ) = 2/3 => (PM)/(PQ) = 2/5]`
2) In ΔOMN and ΔORQ,
`angleOMN = angleORQ` (alternate angles)
`angleMNO = angleOQR` (alternate angles)
=> ΔOMN ~ ΔORQ (AA postulate)
3) `"Area of ΔOMN"/"Area of ΔORQ" = (MN)/(RQ) = 2/5`
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