**Quadrilaterals**

A quadrilateral is a closed plane figure bounded by four line segments. E.g. The figure 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. For example, AC is a diagonal of quadrilateral ABCD.

Types of Quadrilaterals

There are six basic types of quadrilaterals:

1. Rectangle: Opposite sides of a rectangle are parallel and equal. All angles are 90º.

2. Square

Opposite sides of a square are parallel and all sides are equal. All angles are 90º.

3. Parallelogram

Opposite sides of a parallelogram are parallel and equal. Opposite angles are equal.

4. Rhombus

All sides of a rhombus are equal and opposite sides are parallel. Opposite angles of a rhombus are equal. The diagonals of a rhombus bisect each other at right angles.

5. Trapezium

A trapezium has one pair of opposite sides parallel. A regular trapezium has non-parallel sides equal and its base angles are equal, as shown in the following diagram.

6. Kite

Two pairs of adjacent sides of a kite are equal, and one pair of opposite angles are equal. Diagonals intersect at right angles. One diagonal is bisected by the other.

Theorem 3 Prove that the angle sum of a quadrilateral is equal to 360º.

Proof: To prove < A + <B + <C + <D= 360

In tri ABC p + u + B = 180 (angle sum property of triangle)-----1

Similarly

In Tri. ACD , q + v + D = 180--------2

Adding (1 ) and (2)

(p + q) + (u+ v ) + B+ D = 180+ 180

< A + <B + <C + <D= 360

Hence the angle sum of a quadrilateral is 360º.

## 1 comment:

As I know that this is blog where you can find all the definition of maths with diagrams and he main part of math is diagram with out diagram its too difficult to solve equation.properties of parallelograms

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