Define a quadrilateral and find different objects in your school or classroom that have surfaces in the shape of quadrilaterals.

You have read about many types of quadrilaterals. Identify which of them are parallelograms.

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

$X$ 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 $\angle DAC=\angle BCA$