Quadrilateral for Class 9

Understanding quadrilaterals and their classifications is essential for anyone working in fields that involve reasoning and mathematical analysis. From the design of buildings to the development of computer graphics, the significance of quadrilaterals extends across various disciplines. In this chapter, we will go through the parallelogram, square, rectangle, rhombus, trapezium and kite.

Quadrilaterals

A quadrilateral is a polygon with four straight sides and four vertices or corners. The term "quadrilateral" is derived from Latin where “quadri” means “four” and “latus” means “side”. In simple terms, it is a four-sided figure enclosed by four straight segments or edges, forming four angles.

There are different types of quadrilaterals. Each quadrilateral has its own distinctive characteristics.

Parallelogram

1. Definition: A parallelogram is a quadrilateral whose opposite sides are both parallel.
2. Properties: 
   i. Opposite sides are parallel and equal in length.
   ii. Opposite angles are equal.
   iii. Diagonals bisect each other.
   iv. Sum of adjacent angles is 180°.

Rectangle

1. Definition: A rectangle is a parallelogram whose opposite sides are equal and all angles are right angles.
2. Properties:  
   i. Opposite sides are parallel and equal in length.
   ii. All angles are right angles.
   iii. Diagonals are equal and bisect each other.
   iv. Sum of adjacent angles is 180°.

Rhombus

1. Definition: A rhombus is a parallelogram with adjacent sides equal.
2. Properties: 
   i. All sides are equal.
   ii. Opposite sides are parallel.
   iii. Opposite angles are equal.
   iv. Diagonals bisect each other and intersect at right angles (Diagonals are not equal and perpendicular to each other).
   v. Sum of adjacent angles is 180°.

Square

1. Definition: A square is a special parallelogram with all sides equal and all angles at  90°.
2. Properties: 
   i. All sides are equal.
   ii. Opposite sides are parallel.
   iii. Each angle is a right angle.
   iv. Diagonals are equal and intersect at right angles (Diagonals are perpendicular to each other).
   v. Sum of adjacent angles is 180°.

Kite

1. Definition: A kite is a quadrilateral whose two pairs of adjacent sides are equal.
2. Properties:
   i. Adjacent sides are equal in length.
   ii. The sides opposite each other (opposite sides) are not equal in length.
   iii. One pair of opposite angles is equal.
   iv. The diagonals of a kite meet each other at right angles.
   v. Diagonals bisect the angles of a kite.

Trapezium

1. Definition: A trapezium is a quadrilateral with only one pair of opposite sides parallel. 
2. Properties:
   i. A trapezium has a pair of parallel sides known as the bases. The other two sides are not parallel and are called legs and they are typically of different lengths.
   iii. The angles at the bases (parallel sides) are supplementary (180°).
   iv. The perpendicular distance between the bases is known as the height or altitude.

Isosceles Trapezium

1. Definition: An isosceles trapezium is a special trapezium whose one pair of opposite sides is parallel and the non-parallel sides (legs) are equal.
2. Properties:
   i. The angles at the bottom (base angles) of this shape are the same.
   ii. The diagonals are of equal length.

Understanding these shapes and their properties is a crucial part of geometry and various ways to make geometry simpler and more practical.