Question

PQRS is a parallelogram. X and Y are midpoints of sides PQ and Rs respectively. If W and Z are points of intersection of SX & PY and XR and YQ respectively. Then show that ar$\Delta YWZ=ar\Delta XWZ$

Answer 1

X and Y are mid points of PQ and SR
$\Rightarrow$ PXRY is a parallelogram
$\Rightarrow$ XQYS is a parallelogram
$\Rightarrow$ PY || XR
$\Rightarrow$ WY || XZ …(1)
$\Rightarrow$ SX || YQ
$\Rightarrow$ WX || YZ …(2)
From (1) and (2)
XZYW is a parallelogram
WZ is the diagonal
Hence $ar\left(\Delta XZW\right)=ar\left(\Delta YZW\right)$
[ $\because$ diagonal of ||gm divides into two congruent triangles]