Question

X, Y are the mid-points of opposite sides AB and DC respectively of a parallelogram ABCD. AY and DX are intersecting at S; CX and BY are intersecting at R. Then SXRY is a_____________.

• A. Rectangle
• B. Kite
• C. Parallelogram
• D. Square

Answer 1

The correct option is C Parallelogram

Given: $X$ and $Y$ are the mid-points of opposite sides $AB$ and $DC$ of a parallelogram $ABCD.$

$AX=XB$ and $DY=YC$

$AB=DC$

$XB=DY......\left(i\right)$

Also $AB||DC......$(opp. sides of a ïïgm)

$XB||DY.....\left(ii\right)$

Since in quadrilateral $XBYD,XB=DY$ and $XB||DY$

$SYRX$ is a parallelogram.