Quadrilateral

 

Quadrilateral is a simple closed figure with four sides.

Types of quadrilaterals

1. Parallelogram

2. Rectangle

3. Square

4. Rhombus

5. Trapezium

Common property of all quadrilaterals is that the sum of all their angles equals 360°.

Properties of Quadrilaterals

Parallelogram

Parallelogram Properties

Properties of a parallelogram

Formula

· Opposite sides are parallel and congruent.

· Opposite angles are congruent.

· Adjacent angles are supplementary.

· Diagonals bisect each other and each diagonal divides the parallelogram into two congruent triangles.

· If one of the angles of a parallelogram is a right angle then all other angles are right and it becomes a rectangle.

· Area = L * H

· Perimeter = 2(L+B)

 

Rectangles

Parallelogram Properties

Properties of a Rectangle

Formula

· Opposite sides are parallel and congruent.

· All angles are right.

· The diagonals are congruent and bisect each other (divide each other equally).

· Opposite angles formed at the point where diagonals meet are congruent.

· A rectangle is a special type of parallelogram whose angles are right.

· If the length is L and breadth is B, then Length of the diagonal of a rectangle = √(L2 + B2)

· Area = L * B

· Perimeter = 2(L+B)

 

Squares

Parallelogram Properties

Properties of a square

Formula

· All sides and angles are congruent.

· Opposite sides are parallel to each other.

· The diagonals are congruent.

· The diagonals are perpendicular to and bisect each other.

· A square is a special type of parallelogram whose all angles and sides are equal.

· Also, a parallelogram becomes a square when the diagonals are equal and right bisectors of each other.

· If ‘L’ is the length of the side of a square then length of the diagonal = L √2.

· Area = L2.

· Perimeter = 4L

 

Rhombus

Parallelogram Properties

Properties of a Rhombus

Formula

· All sides are congruent.

· Opposite angles are congruent.

· The diagonals are perpendicular to and bisect each other.

· Adjacent angles are supplementary (For eg., ∠A + ∠B = 180°).

· A rhombus is a parallelogram whose diagonals are perpendicular to each other.

· If a and b are the lengths of the diagonals of a rhombus,

· Area = (a* b) / 2

· Perimeter = 4L

 

Trapezium

Parallelogram Properties

Properties of a Trapezium

Formula

· The bases of the trapezium are parallel to each other (MN ⫽ OP).

· No sides, angles and diagonals are congruent.

· Area = (1/2) h (L+L2)

· Perimeter = L + L1 + L2 + L3