Try to draw a parallelogram where three of the angles are right angles but which is not a rectangle. Is such a parallelogram possible? Discuss. 

The interior angles of a quadrilateral are in the ratio $3:5:7:9$, Find the measure of each interior angle.

Prove that if diagonals of a rhombus are equal then it is a square.

Prove that diagonals of a rectangle are of equal length.

Prove that diagonals of a square are equal and they bisect each other at right angles.

$X$ and $Y$ are the midpoints of opposite sides $AB$ and $CD$ of parallelogram $ABCD$. Prove that $AXCY$ is a parallelogram.

In the adjacent figure, $AB$ and $DC$ are two parallel lines which are intersected by transversal $l$ at points $P$ and $R$respectively. Prove that the bisectors of the interior angles make a rectangle.

$ABC$ is an isosceles triangle in which $AB=AC$, $AD$ bisects the exterior angle $PAC$ and $CD\parallel BA$. Prove that $\angle DAC=\angle BCA$