In parallelogram $PQRS$,$PQ = 8 \, \text{cm}$ and $QR = 5 \, \text{cm}$,then the perimeter of $PQRS = \ldots \ldots \ldots$ (in $, \text{cm}$)

Two parallel lines are intersected by a transversal. Show that the quadrilateral formed by the bisectors of interior angles is a rectangle.

In quadrilateral $ABCD$,$AC = BD$ and $AC \perp BD$. If $P, Q, R$ and $S$ are the midpoints of the sides $AB, BC, CD$ and $DA$ respectively,prove that $PQRS$ is a square.

In $\Delta ABC$,$P$ and $Q$ are the midpoints of $AB$ and $AC$ respectively. If $PQ + BC = 8.4 \, cm$ and $AB + AC = 20.5 \, cm$,then find the perimeter of $\Delta ABC$ in $cm$.

In $\Delta ABC$,$P$ and $Q$ are the midpoints of $AB$ and $AC$ respectively. If $BC + PQ = 21 \text{ cm}$,then find the length of $BC$.

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