Prove that each angle of a rectangle is $90°$.

Prove that the bisectors of any two adjacent angles of a parallelogram are at right angles.

$\mathrm{ABCD}$ is a rectangle in which diagonal $BD$ bisects $\angle B$. Show that $ABCD$ is a square.

If $\mathrm{P}$ and $\mathrm{Q}$ are points of trisection of the diagonal $\mathrm{BD}$ of a parallelogram $\mathrm{ABCD}$. Prove that $\mathrm{CQ}\parallel \mathrm{AP}$.