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 = √(L^{2} + B^{2})

- 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 = L
^{2}. - 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+L
_{2}) - Perimeter = L + L
_{1}+ L_{2}+ L_{3}

## 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

Do opposite sides in a quadrilateral have to be equal in order for it to have diagonals that are perpendicular?