Name the quadrilaterals whose diagonals.

(i) Bisect each other

(ii) Are perpendicular bisectors of each other

(iii) Are equal

In the figure given below, a rectangle of perimeter $76$ units is divided into $7$ congruent rectangles:

What is the perimeter of each of the smaller rectangles?

Let $ABCD$ be a square. An arc of a circle with $A$ as centre and $AB$ as radius is drawn inside the square joining the points $B$ and $D$. Points $P$ on $AB, S$ on $AD, Q$ and $R$ on arc $BD$ are taken such that $PQRS$ is a square. Further suppose that $PQ$ and $RS$ are parallel to $AC$. Then, $\frac{\text{ area }PQRS}{\text{ area }ABCD}$ is

The three angles of a quadrilateral are $76°, 54° \mathrm{and} 108°$. Find the measure of the fourth angle.

The angles of a quadrilateral are in the ratio $1:2:3:4$. Find the measure of each angle.

The angles of a quadrilateral are in the ratio $3:5:7:9$. Find the measure of each of these angles.

The quadrilateral formed by angle bisectors of a cyclic quadrilateral is a

The angles of a quadrilateral are respectively $120°$, $75°$ and $135°$, the measure of fourth angle is:

A quadrilateral has three acute angles, each measuring $75°$. Find the measure of the fourth angle.

In the adjacent figure, the bisectors of $\angle A$ and $\angle B$ meet in a point $P$. If $\angle C=100°$ and $\angle D=60°$, find the measure of $\angle APB$.

Prove that if the diagonals of a parallelogram intersect at right angles, then it is a rhombus.