$ABCD$ is a parallelogram. If its diagonals are equal,then find the value of $\angle ABC$. (in $^{\circ}$)

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

In parallelogram $ABCD$,two points $P$ and $Q$ are taken on diagonal $BD$ such that $DP = BQ$ (see figure). Show that: $\Delta AQB \cong \Delta CPD$.

$(1)$ The diagonals of a rhombus are ....... to each other.
$(2)$ The diagonals of a parallelogram ...... each other.

In a parallelogram $ABCD$,$\angle A = 5 \angle B$,then $\angle C = \ldots$ (in $^o$)

Show that each angle of a rectangle is a right angle.