# Introduction

## NECESSARY CONDITIONS OF A PARALLELOGRAM

• In a parallelogram, opposite sides are equal.
• In a parallelogram, opposite angles are equal.
• The diagonals of a parallelogram bisect each other.
• A closed figure having four sides, four angles and four vertices is called a quadrilateral.
• The sum of the four angles of a quadrilateral is 360°.

### TYPES OF QUADRILATERALS

Trapezium: If one pair of opposite sides of a quadrilateral are parallel, then the quadrilateral is called a trapezium.

Parallelogram: If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram.

Rectangle: In a parallelogram, if one angle is right angle, then the quadrilateral is called a rectangle.

Rhombus: In a parallelogram if all the four sides be equal, then the quadrilateral is a rhombus.

Square: In a quadrilateral if all the four sides are equal and one angle is right angle, then all the other three angles are also right angles. Such a quadrilateral is called a square.

### SUFFICIENT CONDITIONS FOR A QUADRILATERAL TO BE PARALLELOGRAM

• &If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.
• If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.
• If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
• A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel.