Quadrilateral: Definition, Types, Parallelogram, Rhombus, Rectangle and Square

A quadrilateral is a topic in Euclidean geometry, which deals with polygons that contain four vertices and four sides. Quadrilaterals are of 2-dimensional structures. They can be classified into five major types. Trapezium The trapezium is a 2-dimensional shape that has a pair of parallel sides. NCERT Class 9 Maths Chapter 8 Quadrilaterals deals with the Angle Sum Property of a Quadrilateral, Types of Quadrilaterals such as Trapezium, Parallelograms, Rectangle, Rhombus, Square, and Kite. It further elucidates the Properties of a Parallelogram and Conditions for a Quadrilateral to be a Parallelogram.For example, in an isosceles trapezium, the angles on the opposite sides parallel to each other are equal. These angles are commonly known as the base angles.

Features of Trapezium

• The trapezium’s base and the side opposite to it are parallel.
• The angles, diagonals and sides are not equal (except in the case of an isosceles trapezium).

Parallelogram

A figure that has opposite sides parallel to each other is known as a parallelogram. Apart from that, the sides opposite to each other are equal.

Features of Parallelogram

• The opposite sides are equal as well as parallel to each other.
• They have congruent angles.
• The angles present in the adjacent side of theThe following are some of the important formulae for trapezium,
• Perimeter of Trapezium = L1+L2+L3+L4
• Area of Trapezium = 12 h (L1+L2)
• parallelogram are supplementary.
• If an angle present in the parallelogram is 90°, then by opposite angle property and the supplementary nature, other angles in the parallelogram are also 90°, making the parallelogram a rectangle.
• The diagonals of a parallelogram bisect each other and divide the figure into two congruent triangles.

Figure of a Parallelogram

The given below are some of the fundamental formulae related to a parallelogram
Perimeter of parallelogram = 2 (L + B)
Area of Parallelogram = L * H

Rhombus

A rhombus has all its four sides equal in terms of length. Therefore, diagonals present in a rhombus are perpendicular bisectors to one another.

Features of Rhombus

• The rhombus has all four equal sides.
• Rhombus has congruent angles on its opposite sides.
• The adjacent angles present are supplementary.
• Rhombus’s diagonals are perpendicular bisectors of each other.
• A rhombus is considered a special type of parallelogram.

If m and n are the diagonals of a rhombus, then,

Perimeter of Rhombus = 4 L
Area of Rhombus = (a * b) / 2

Rectangle

A rectangle is another type of parallelogram that has all the angles equal to right angles. In a rectangle, opposite sides have the same length.

Properties of Rectangle

• Rectangle has its parallel opposite sides and is congruent.
• All angles contained in a rectangle are right angles.
• They have diagonals that bisect each other.

Following are the formulae related to rectangle,

Perimeter of Rectangle = 2 (L + B)
Area of Rectangle = L * B

Square

A square is one of the most basic shapes in a quadrilateral that contains four equal sides in terms of length. All the four angles present in a square are also equal. Therefore, they are all right angles.
Properties of Square

• All angles and sides are congruent to one another.
• A square has parallel opposite sides.
• Diagonals present in a square are congruent as well.
• Diagonals are perpendicular bisectors of each other.
• A square can be regarded as a unique parallelogram with its angles and sides equal to each other.

Formulae related to the square are mentioned below,

Perimeter of Square = 4 L
Are of Square = L2