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Quadrilaterals

A quadrilateral is a 2-dimensional closed shape with four straight sides. E.g. The shape

ABCD shown here is a quadrilateral.

A line segment drawn from one vertex of a quadrilateral to the opposite vertex is called a

diagonal of the quadrilateral. AC is a diagonal of quadrilateral ABCD, as is BD.

TYPES & PROPERTIES OF QUADRILATERALS

There are seven types of quadrilaterals that can be divided into two groups:

parallelograms and other quadrilaterals.

1. Parallelograms

Quadrilaterals are called parallelograms if both pairs of opposite sides are equal andparallel to each other. Different parallelograms and their properties are described below.

a) Parallelogram

Opposite sides of a parallelogram are parallel and equal in length.Opposite angles are equal in size.

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b) RectangleOpposite sides of a rectangle are parallel and equal in length.

All angles are equal to 90.

c) Square

Opposite sides of a square are parallel and all sides are equal in length.All angles are equal to 90.

d) RhombusAll sides of a rhombus are equal in length

Opposite sides are parallel.Opposite angles of a rhombus are equal.

The diagonals of a rhombus bisect each other at right angles.

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Rectangles, squares and rhombuses (or diamonds) are parallelograms.

2.Other Quadrilaterals

Other quadrilaterals include trapeziums, kites and irregular quadrilaterals.

a) TrapeziumA trapezium has one pair of opposite sides parallel.

A regular trapezium has non-parallel sides equal and its base angles are equal, as shownin the diagram.

b) KiteTwo pairs of adjacent sides of a kite are equal in length

One pair of opposite angles (the ones that are between the sides of unequal length) areequal in size.

One diagonal bisects the other.Diagonals intersect at right angles.

3. Irregular Quadrilateral

An irregular quadrilateral does not have any special properties.

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Angle Sum of a Quadrilateral is 360.

Draw a quadrilateral ABCD. Then draw the diagonal AC to form two triangles.

Finding the Fourth Angle of a Quadrilateral

If the measurements of three angles of a quadrilateral are known, then the missing angle

can be calculated.

Here are the things to remember

All quadrilaterals have 4 sides

A square has got 4 sides of equal length and 4 right angles (right angle = 90 degrees).

A Rhombus has got 4 sides of equal length and opposite sides are parallel and angles areequal.

The rectangle (oblong) contains 4 right angles (an angle of 90). It has got 2 pairs of

equal length sides

A parallelogram is a rectangle that has been pushed over. Opposite sides are the samelength and they are parrallel.

A trapezium as got one pair of parallel sides.

A kite as got two pairs of sides next to each other that have equal length.

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BY

ASHOK KUMAR GOVT.SR.SEC.SCHOOL,

(MATHS MASTER) GAKHAL-DHALIWAL,JALANDHAR)

PICTUR

ES FR

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