## Chapter: 8

## What Are Quadrilaterals ?

## Quadrilateral

A closed figure obtained by joining four non-collinear points is called a quadrilateral.

**Angle Sum Property of a Quadrilateral :**

Sum of all angles of a quadrilateral is 360°

## Types Of Quadrilaterals

**Parallelogram:**

(i) Opposite sides are equal

(ii) Opposite angles are equal

(iii) Diagonals bisect each other

(iv) A pair of opposite sides is equal and parallel.

(v) Diagonals divide it into two congruent triangles.

**Rectangle:**

(i) diagonls are equal

(ii) each angle is 90°

**Square:**

(i) diagonls are equal

(ii) each angle is 90°

(iii) all sides are equal

**Rhombus:**

(i) diagonals bisect each other at right angles

(ii) all sides are equal

**Trapezium:**

(i) One pair of opposite sides is parallel

(ii) Other pair of opposite sides is non-parallel

**Isosceles Trapezium:**

(i) Two non-parallel sides are equal

(ii) one pair of opposite side is equal

**Kite:**

(i) Kite has pair of equal adjacent sides.

(ii) It is not a parallelogram

## Important Points To Remember

• The diagonals of a parallelogram are equal if and only if it is a rectangle.

• If a diagonal of a parallelogram bisects one of the angles of the parallelogram then it also bisects the opposite angle.

• In a parallelogram, the bisectors of any two conssecutive angles interesect at a right angle.

• The angle bisectors of a parallelogram form a rectangle.

## Mid Point Theorem

A line segment joining the mid points of any two sides of a triangle is parallel to the third side and length of the line segment is half of the parallel side.

## Converse

A line through the mid point of a side of a triangle parallel to another side bisects the third side.

## Intercept Theorem

If there are three parallel lines and the intercepts made by them on one transversal are equal then the intercepts on any other transversal are also equal.