Types of quadrilaterals and its properties — lesson. Mathematics State Board, Class 9.

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There are various types of quadrilaterals. They are:

A square is a quadrilateral with four equal sides and four right angles.

A square has:

four equal sides $AB=BC=CD=DA$ .
four right angles $∠A=∠B=∠C=∠D=90°$ .
two pairs of parallel sides $AB∥DC$ and $AD∥BC$ .
two equal diagonals $AC=BD$ .
diagonals that are perpendicular to each other $AC⊥BD$ .
diagonals that bisect each other. That is one diagonal divides the other diagonal into exactly two halves.

A rectangle is a quadrilateral with two pairs of equal and parallel opposite sides and four right angles.

A rectangle has:

two pairs of parallel sides $AB∥DC$ and $AD∥BC$ .
four right angles $∠A=∠B=∠C=∠D=90°$ .
opposite sides of equal lengths $AB=DC$ and $AD=BC$
two equal diagonals $AC=BD$
diagonals that bisect each other. That is one diagonal divides the other diagonal into exactly two halves.

A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.

A parallelogram has:

two pairs of parallel sides $PQ∥RT$ and $PR∥QT$ .
opposite sides of equal lengths $PQ=RT$ and $PR=QT$ .
opposite angles that are equal $∠P=∠T$ and $∠Q=∠R$ .
two diagonals that bisect each other. That is one diagonal divides the other diagonal into exactly two halves.

A trapezium is a quadrilateral in which one pair of opposite sides is parallel.

In the above figure,

$EF$ and

$GH$ are bases.

In the above figure,

$EG$ and

$FH$ are legs.

There is nothing special about the sides, angles, or diagonals of a trapezium.

But if the two non-parallel opposite sides are of equal length, then it is called an isosceles trapezium.

The above quadrilateral

$XYZW$ is an isosceles trapezium.

In an isosceles trapezium, the lengths of the diagonals are equal. That is

$XZ=WY$ .

A rhombus is a quadrilateral with four equal sides.

A rhombus has:

two pairs of parallel sides $EH∥FG$ and $EF∥HG$ .
four equal sides $EH=HG=GF=FE$ .
opposite angles are equal $∠E=∠G$ and $∠H=∠F$ .
diagonals that are perpendicular to each other $EG⊥HF$ .
diagonals that bisect each other. That is one diagonal divides the other diagonal into exactly two halves.

A kite is a quadrilateral in which two pairs of adjacent sides are equal.

A kite has:

The following chart allows us to understand the hierarchy of quadrilaterals.

Did you find an error?

2. Types of quadrilaterals and its properties