cbse maths types of Quadrilateral
Quadrilaterals
A quadrilateral is a closed plane figure bounded by four line segments. E.g. The figure ABCD shown here is a quadrilateral.
A line segment drawn from one vertex of a quadrilateral to the opposite vertex is called a diagonal of the quadrilateral. For example, AC is a diagonal of quadrilateral ABCD.
Types of Quadrilaterals
There are six basic types of quadrilaterals:
1. Rectangle: Opposite sides of a rectangle are parallel and equal. All angles are 90º.
2. Square
Opposite sides of a square are parallel and all sides are equal. All angles are 90º.
3. Parallelogram
Opposite sides of a parallelogram are parallel and equal. Opposite angles are equal.
4. Rhombus
All sides of a rhombus are equal and opposite sides are parallel. Opposite angles of a rhombus are equal. The diagonals of a rhombus bisect each other at right angles.
5. Trapezium
A trapezium has one pair of opposite sides parallel. A regular trapezium has non-parallel sides equal and its base angles are equal, as shown in the following diagram.
Theorem 3 Prove that the angle sum of a quadrilateral is equal to 360º.
Proof: To prove < A + <B + <C + <D= 360
In tri ABC p + u + B = 180 (angle sum property of triangle)-----1
Similarly
In Tri. ACD , q + v + D = 180--------2
Adding (1 ) and (2)
(p + q) + (u+ v ) + B+ D = 180+ 180
< A + <B + <C + <D= 360
A quadrilateral is a closed plane figure bounded by four line segments. E.g. The figure ABCD shown here is a quadrilateral.
A line segment drawn from one vertex of a quadrilateral to the opposite vertex is called a diagonal of the quadrilateral. For example, AC is a diagonal of quadrilateral ABCD.
Types of Quadrilaterals
There are six basic types of quadrilaterals:
1. Rectangle: Opposite sides of a rectangle are parallel and equal. All angles are 90º.
2. Square
Opposite sides of a square are parallel and all sides are equal. All angles are 90º.
3. Parallelogram
Opposite sides of a parallelogram are parallel and equal. Opposite angles are equal.
4. Rhombus
All sides of a rhombus are equal and opposite sides are parallel. Opposite angles of a rhombus are equal. The diagonals of a rhombus bisect each other at right angles.
5. Trapezium
A trapezium has one pair of opposite sides parallel. A regular trapezium has non-parallel sides equal and its base angles are equal, as shown in the following diagram.
6. Kite
Two pairs of adjacent sides of a kite are equal, and one pair of opposite angles are equal. Diagonals intersect at right angles. One diagonal is bisected by the other.
Theorem 3 Prove that the angle sum of a quadrilateral is equal to 360º.
Proof: To prove < A + <B + <C + <D= 360
In tri ABC p + u + B = 180 (angle sum property of triangle)-----1
Similarly
In Tri. ACD , q + v + D = 180--------2
Adding (1 ) and (2)
(p + q) + (u+ v ) + B+ D = 180+ 180
< A + <B + <C + <D= 360
Hence the angle sum of a quadrilateral is 360º.
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