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Quadrilateral is a geometric shape which has four sides and four vertices.

• Trapezium
• Rhombus
• Parallelogram
• Square
• Rectangle

### TRAPEZIUM

1. A Trapezium is a quadrilateral which has two parallel sides in either of the directions.

Side 1” and “Side 2” are parallel in above figures.

### Regular and Irregular Polygon

#### Definition of Regular Polygon

A quadrilateral is said to be regular Polygon if all angles are equal and all sides are equal.

Examples of Regular polygon are

1. Square
2. Equilateral Triangle
3. Regular Pentagon
4. Hexagon

#### Irregular Polygon

whereas in irregular polygon either the sides are not equal or the angles are not equal.

Examples of irregular polygon are

1. Rectangle.- All the angles in rectangle are 90 degrees but only opposite sides are equal.

2. Isoceles or obtuse angled triangle etc.

### Angle Sum Property

Simply put sum of all the angles in a triangle is 180 degrees.

How to find Interior angles of any quadrilateral ?

Divide shape into equal triangles . See video below

Sum of measures of all exterior angles of polygon is 360 degrees.

Remember
##### Types and Properties of Quadrilateral
• Regular Trapezium
• Square
• Rectangle
• Parallelogram
• Rhombus
• Kite

Regular Trapezium – Trapezium is a quadrilateral with one pair of parallel sides.

Isoceles trapezium is one in which non parallel sides of trapezium are equal in length.

Square

• All the four sides of square are equal.
• All the four angles are of 90 degrees.
• Opposite sides are parallel.
• Diagonals bisect each other at 90 deg.i.e perpendicular to each other.

Rectangle :

• Opposite sides of rectangle are equal and Parallel.
• All the angles in rectangle are 90 degrees.
• Diagonals of rectangle are of equal length.

Parallelogram : –

• Opposite sides of parallelogram are equal and parallel.
• The diagonals do not bisect at 90 degrees.
• Opposite angles of parallelogram are equal by Angle side angle congruency.

Rhombus :-

• All sides are equal in rhombus.
• Diagonal bisect each other at 90 degrees.
• All sides are equal in rhombus.
• Opposite sides are parallel.

Kite : –

• Adjacent sides of kite are equal.
• Diagonals bisect at 90 degrees.