Quadrilaterals Properties | Parallelograms, Trapezium, Rhombus

In this tutorial on basic geometry concepts, we cover the types and properties of quadrilaterals: Parallelogram, rectangle, square, rhombus, trapezium.

Definition:

A quadrilateral is a simple closed figure with four sides.

Types of quadrilaterals

There are five types of quadrilaterals.

• Parallelogram
• Rectangle
• Square
• Rhombus
• Trapezium

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

Let us look into the properties of different quadrilaterals.

Parallelogram

Properties of a parallelogram

• 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.

Important formulas of parallelograms

• Area = L * H
• Perimeter = 2(L+B)

Rectangles

Properties of a Rectangle

• 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.

Important formulas for rectangles

• 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

Properties of a square

• 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.

Important formulas for Squares

• If ‘L’ is the length of the side of a square then length of the diagonal = L √2.
• Area = L2.
• Perimeter = 4L

Rhombus

Properties of a Rhombus

• 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.

Important formulas for a Rhombus

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

• Area = (a* b) / 2
• Perimeter = 4L

Trapezium

Properties of a Trapezium

• The bases of the trapezium are parallel to each other (MN ⫽ OP).
• No sides, angles and diagonals are congruent.

Important Formulas for a Trapezium

• Area = (1/2) h (L+L2)
• Perimeter = L + L1 + L2 + L3

Summary of properties

Summarizing what we have learnt so far for easy reference and remembrance:

S.No.	Property	Parallelogram	Rectangle	Rhombus	Square
1	All sides are congruent	✕	✕	✓	✓
2	Opposite sides are parallel and congruent	✓	✓	✓	✓
3	All angles are congruent	✕	✓	✕	✓
4	Opposite angles are congruent	✓	✓	✓	✓
5	Diagonals are congruent	✕	✓	✕	✓
6	Diagonals are perpendicular	✕	✕	✓	✓
7	Diagonals bisect each other	✓	✓	✓	✓
8	Adjacent angles are supplementary	✓	✓	✓	✓

Continue learning more about: – Properties of Lines and Angles – Properties and formulas of Circles – Types of Triangles and Properties