#### 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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#### APPEARS IN

Solution In δPqr, Mn is Parallel to Qr and `(Pm)/(Mq) = 2/3` and Find `(Mn)/(Qr)` and Prove that Triangle Omn and Triangle Orq Are Similar Concept: Similarity of Triangles.