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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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## 36 Comments

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

However, in a kite the diagonals are perpendicular but the diagonals are not congruent. In a rhombus, rectangle or square for it to have diagonals that is perpendicular and congruent all of its sides must be congruent. In the case of kite, of all of its sides are congruent it will become either a rhombus or a square.

Do the diagonals of a trapezium bisect each other?

Thanks this was so helpful for me

No all sides of a quadrilateral should be congruent for the diagonals to be perpendicular

No

Diagonal will be perpendicular only when all sides are equal not opposite sides.

Hey mate

Herez your answer

If opposite sides would be equal in a quadrilateral still there is no any surity that the diagonals will be perpendicular

For eg a paralleogram type quadrilateral whose

opposite sides are equall but its doagonal

Are not perpendicular.

But if all the side became equal in a quadrilateral then therez the surity that the diagonal will be perpenficular

Eg rhombus or square

Tynxx

Actually not, for example kites dont have opposite sides equal but both of its diagonals are perpendicular.

Simply we can say that if a quadrilateral have opposite sides equal then its diagonal will bisect each other.

And if its adjacent sides are equal then they cut each other perpendicularly.

Correct me if wrong

no all sides must be equal

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

No they are never same. The are always different .

If they will be equal it will not be a trapezium

Not necessarily equal

Sometimes it’s equal then the trapezium is called isotrapezium.

are the diagonals of the rectangles are congruent?

how to proof it?

Since the opposite sides of a rectangle are congruent, it’s diagonals are also congruent. This can be done by applying Pythagoras theorem..

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

Yes we can proove it by sas method as diagnols bisect parrellelograms into 2 equal halves. and opp angles and sides are equal

If ab =33 bc =27 CD = 33 DA=21 area of quadrilateral ?

Area of the quadrilateral = Area of rectangle + Area of Right angled triangle

Length of the rectangle = 33cm

Breadth of the rectangle = 21cm

Area of rectangle = Length x Breadth

= 33 x 21

= 693 sq. cm

Now in right angled triangle,

Hypotenuse = 33cm

Base = 6cm

Therefore, the height of the triangle = Square root of (square of hypotenuse – square of base) [ By Pythagoras Theorem ]

= Square root of(33 x 33 – 6 x 6)

= Square root of 1053

= 32.44cm

Area of Right angled Triangle = 1/2 x base x height

= 1/2 x (27-21) x 32.44

= 1/2 x 6 x 32.44

= 97.32 sq. cm

So, Area of the quadrilateral = Area of rectangle + Area of Right angled triangle

= 693 + 97.32

= 790.32 sq. cm

Why are you asking because it is quite easy?

You know that when the heights of quadrilateral are given which will perpendicular to any one of diagonal then fomula for area is given by

=1/2×(h1+h2)×diagonal

What are the names of the three different quadrilaterals with two congruent

diagonals?

Explain the sum of properties of quadrilateral is 360 degree.

Are diagonals the bisectors of angles in a quadrilateral or parallelogram?

Parallelogram

Does a parallelogram have a Line of symmetry?

Is parallelogram a trapezium?

Never a parallelogram be a trapezium.

A parallelogram can form a rectangle.

can a parallelogram named as trapezium, as we are saying all reactangles are parallelograms

No but it’s reverse is true

I have an query on trapezium

If a angle of a trapezium is 90°then what is it called

Rectangle OR square

squares are my favourite type of quadrilaterals

Why so much confusion 1) Square, Rhombus & kite have the diagonals at right angles to each other.

But what do you call a quadrilateral that is not a parallelogram with one diagonal that divides the quadrilateral into two congruent triangles