Quadrilaterals

If a quadrilateral (with one set of parallel sides) is an isosceles trapezoid, its legs are congruent.

What is diagonal of Quadrilateral and write the number of diagonals of a rectangle.

If $KJ=4 \mathrm{cm}, JM=7 \mathrm{cm}$, then find $LK$ in the kite $KJML$.

All the interior angles of rectangle are right angles.

All the sides of rectangle are equal in length. 

$ABCD$ is a rhombus. Prove that the diagonals of the rhombus bisect each other and hence find $CO$ if $AO=3 \mathrm{cm}$. 

$ABCD$ is a rhombus. Prove that the diagonals of the rhombus bisect each other and hence find $DO$ if $BO=4 \mathrm{cm}$. 

$ABCD$ is a kite. Find $\angle AOB$ in the number of degrees.

Prove that the diagonals of a kite are perpendicular to each other.

Prove that if a quadrilateral (with one set of parallel sides) is an isosceles trapezoid, its legs are congruent.

$AB$ and $BC$ are two of the eight sides of a regular octagon. An isosceles triangle $ABP$, in which $AP=BP$, is drawn on $AB$, such that the $∆ABP$ and the octagon are on opposite sides of $AB$. If $\angle ABP=72°$ , calculate $\angle PBC$.

Two angles of a convex polygon are right angles and each of other is $120°$. How many sides has the polygon?

Three of the exterior angles of a hexagon are $40°, 51°, 86°$ each. If each of the remaining exterior angle is $x$, calculate the value of $x$ 

One angle of a pentagon is $140°$. If the remaining angles are in the ratio $1:2:3:4$, calculate the measure of the greatest angle. 

All the sides of rectangle are equal.

In a quadrilateral $ABCD$, $AB=CD$ and $\angle B=\angle C$. Prove that $AD\parallel BC$.

The perimeter of one square is $748 \mathrm{cm}$ and that of another is $336 \mathrm{cm}$ . Find the perimeter and the diagonal of a square which is equal in area to the sum of these two.

$ABCDE$ is a regular pentagon. Diagonal $AD$  divides $\angle CDE$ into two parts. Find the ratio $\frac{\angle ADE}{\angle ADC}$.

Two alternate sides of a regular polygon, when produced, meet at right angle. Find  the value of each exterior angle of the polygon.

 In a pentagon $ABCDE,$ $BC\parallel ED$and $\angle B : \angle A : \angle E = 5 : 3 : 4.$ Find the measure of $\angle B$.