If one angle of a parallelogram is a right angle, prove that all other angles are right angles​.

$ABCD$ is a rhombus in the given figure. $RABS$ is a straight line such that $RA=AB=BS$, Prove that $RD and SC$ when produced meet at right angle.

Prove that the bisector of the interior angle of a rectangle form a square.

$M and N$ points are taken on the diagonal $AC$ of a parallelogram $ABCD$ such that $AM=CN$. Prove that $BMDN$ is a parallelogram.

In the given figure, $AP$ is bisector of $\angle A$ and $CQ$ is bisector of $\angle C$ of parallelogram $ABCD$. Prove that $APCQ$ is a parallelogram.

In a $\square ABCD$, $AB=AD$ and $CB=CD$. Prove that $AC$ bisects $\angle BAD$.

In $\square ABCD$, $AB=AD$ and $CB=CD$, Prove that $AC$ is perpendicular bisector of $BD$.

In the given figure, $ABCD$ is a trapezium in which $DA\parallel CB$. $AB$ has been produced to $E$. Find the angles of the trapezium.