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

A quadrilateral is a simple closed figure with four sides.

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.

- 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)

- 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 = √(L^{2} + B^{2})

- Area = L * B
- Perimeter = 2(L+B)

- 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 = L
^{2}. - Perimeter = 4L

- 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

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

- Area = (1/2) h (L+L
_{2}) - Perimeter = L + L
_{1}+ L_{2}+ L_{3}

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

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## 11 Comments

Very simple and easy to learn from this website

Thanks!!

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

Yes when sides on opposite are equal then only the diagnols perpendicularly bisect each other

It is not correct.The diagonals are perpendicular if and only if all the sides are equal as in the case of a rhombus or a square.

The diagonals will be perpendicular also if the pairs of adjacent sides are equal as in the case of a kite

Are the measure of a pair of parallel sides in a trapezium equal?

No they are not.

If they were, it would become a parallelogram and a trapezium is not a parallelogram

The angle of quadrilateral is sub set of quadrilateral ?

my answer is no.

but still not get whole explanation.

pls explain

You Forgot one Quadrilateral : Kite

In trapezium only one pair of opposite sides are parallel

are the diagonals of the rectangles are congruent?

how to proof it?

Take a triangle with common base from that dignols and made that triangle congruent by sas then both side will be equal by cpct