# TrianglePQR and triangleXYZ are such that PQ||XY, PR||XZ and PQ=XY. if PR=XZ, then show that area of (trianglePQR)=area of(triangleXYZ)

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by Jasra

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by Jasra

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See:-

PQ II XY , PRIIXZ ,and the mentioned sides are of equal length.

Lines are parallel and intersecting at a common point subtend the same angle at the points of intersection.Lines being of equl length..their bases - QP and YZ are also of equal length..Hence both the triangles are same and hence equal areas..

In ΔPQR and XYZ

PQ = XY

PR = XZ

∠Q = ∠Y (QX as transversal)

∴ΔPQR =Δ XYZ

⇒ar(PQR) = ar (XYZ)

PQ = XY

PR = XZ

∠Q = ∠Y (QX as transversal)

∴ΔPQR =Δ XYZ

⇒ar(PQR) = ar (XYZ)