Types of Quadrilateral and their properties

Quadrilateral: A quadrilateral is a four-sided closed figure having four vertices, four angles, and two diagonals.

In the given figure ABCD is a quadrilateral

The sum of four angles of the quadrilateral is always 360 º i.e ∠A+∠B+∠C+∠D=360º

There are six types of quadrilaterals based on their Properties. Let’s discuss them one -by-one

1. Rectangle

A Quadrilateral is knowns as Rectangle when its opposite sides are parallel and each angle measure is 90 º.In the given figure, ABCD is  a rectangle whose opposite sides are parallel i.e AB||CD and AD|| BC and each angle is a right angle

Properties of Rectangle

1. The opposite side of the Rectangle are parallel and equal

2. Each angle of the Rectangle is a right angle

3. The diagonal of a rectangle bisect each other and are equal in length

2. Square

Remember this: A square is a rectangle in which rectangle all sides are equal

That’s why the definition of Square and Rectangle are the almost same

A Quadrilateral is knowns as Rectangle when its opposite sides are parallel and each angle measure is 90 º.In the given figure ABCD is a square , Whose AB||CD and AD|| BC and each angle is a right angle

Properties of square

• The opposite sides of the square are parallel.
• All four sides of a square are equal whereas In a rectangle only the Opposite side are equal
• Each angle of the square is a right angle
• Diagonals of a square bisect each other at 90 º and are equal in size

3. Parallelogram

A quadrilateral is known as a Parallelogram(write as llgm )  when its opposite sides are parallel and opposite angles are equal.

In the given figure ,ABCD is a llgm whose opposite side is parallel AB||CD and AD|| BC and opposite angles are equal ∠A=∠C and ∠B=∠D

Properties of Parallelogram

• The opposite side of the parallelogram are parallel and equal
• Opposite angles of a parallelogram are equal
• Diagonal of llgm bisect each other but no are equal in length
• Pairs of adjacent angles are supplementary i.e 180º

4. Rhombus

Note:Rhombus is a parallelogram in which all four sides are equal

A quadrilateral is known as Rhombus when its opposite sides are parallel and opposite angles are equal . The difference between Rhombus and parallelogram is,

Rhombus all sides are equal whereas parallelogram has only opposite sides equal

Properties of Rhombus

• All sides of a rhombus are equal
• opposite sides of a rhombus are parallel
• opposite angles of a rhombus are equal
• Diagonals of a rhombus bisect each other at a right angle

You have noticed some similarity in these four quadrilaterals to each other because these are related to each other

Notes:

• A square is a rhombus but a rhombus may not be a square
• A square is a rectangle but a rectangle may not be a square
• A square is a parallelogram but a parallelogram may not be a square

5. Trapezium

A quadrilateral is an as known a Trapezium whose one pair of sides are parallel and equal to each other. In the given figure, ABCD is a trapezium because AB||CD and AB=CD

Properties of Trapezium

• One side of a trapezium is parallel and equal
• When non-parallel sides and base angle are equal, then it’s known as regular Trapezium

6. Kite

A quadrilateral is known as Kite whose two pairs of adjacent sides are equal  . In the given figure, ABCD is a kite because its adjacent sides are equal

Properties of kite

• Two pairs of adjacent sides are equal
• One pair of opposite angles are equal
• The longest diagonal bisect the shortest diagonal at the right angle