Question

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)

Answer 1

Infact both the triangles are totally same.Hence same area.
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..

Answer 2

In ΔPQR and  XYZ

PQ = XY
PR = XZ
∠Q = ∠Y (QX as transversal) 

∴ΔPQR =Δ  XYZ

⇒ar(PQR) = ar (XYZ)