Quadrilaterals shape & its properties

8th May 2020
Math

Quadrilaterals

Quadrilaterals shape & its properties

Quadrilateral :

A quadrilateral is closed 2-Dimensional shape whose covered with four sides-

  1. Rectangle.
  2. Square.
  3. Rhombus.
  4. Paralellogram.

Quadrilaterals shape & its properties

1.Rectangle:

A Quadrilateral with four sides that in which opposite sides are parallel and equal to each other and also this shape contained four right angles. So, this type of quadrilateral is known as a Rectangle.

Conditions:

  1. opposite sides are equal.
  2. Diagonals are also equal.
  3. Opposite sides are parallel to each other.
  4. Containing four right angles with adjacent sides.
Quadrilateral: Rectangle

In figure— 

Let PQRS be the rectangle

1.PQ = RS  and PR = QS

2.QR = PS.

3.PQ || RS  and   PR || QS.

4.∠PQR = ∠RPQ = ∠QSR = ∠SRP = 90°

                    Area of Rectangle :

Area = width .height

Or another word be can say that the area of rectangle is multiplication of adjacent sides.

2.Square:

A Quadrilateral with four sides that in which all sides are parallel and equal to each other and also this shape contained four right angles. So, this type of quadrilateral is known as a Square.

                      Or

A rectangle becomes a Square when all sides are equal to each other.

Conditions:

  1. All sides are equal.
  2. Diagonals are also equal.
  3. Opposite sides are parallel to each other.
  4. Containing four right angles with adjacent sides.
Quadrilateral: Square

In figure— 

Let PQRS be the Square.

  1. PQ = RS = PR = QS ( sides)
  2. QR = PS. ( diagonals )
  3. PQ || RS  and   PR || QS.
  4. ∠PQR = ∠RPQ = ∠QSR = ∠SRP = 90°

Area of Square :

Area = width .height ; ( width = height )

Or another word be can say that the area of Square is multiplication of adjacent sides.

3.Rhombus:

Rhombus: A Quadrilateral with four sides that in which four sides are equal and opposite sides are parallel to each  other and also opposite angles are equal to each other. So, this type of quadrilateral is known as a Rhombus.

Conditions:

    1. All sides are equal.
    2. Diagonals are not equal.
    3. Opposite sides are parallel to each other.
    4. opposite angles are equal to each other.
Quadrilateral: Rhombus

In figure— 

Let PQRS be the Rhombus.

    1. PQ = RS = PR = QS ( sides are equal)
    2. QR  ≠  PS. ( diagonals are not equal)
    3. PQ || RS  and   PR || QS.
    4. ∠RPQ = ∠QSR  and ∠PQR = ∠SRP

Note :  Rhombus is a Square if and only if all angles right angle.

4.Parallelogram:

Parallelogram : A Quadrilateral with four sides that in which  opposite sides are equal and parallel to each  other and also opposite angles are equal to each other. So, this type of quadrilateral is known as a Rhombus.

Conditions:

    1. Opposite sides are equal.
    2. Diagonals are not equal.
    3. Opposite sides are parallel to each other.
    4. opposite angles are equal to each other.
Quadrilateral: parallelogram

In figure— 

Let PQRS be the Parallelogram.

    1. PQ = RS & PR = QS (side length)
    2. QS  ≠  PR. ( diagonals are not equal)
    3. PQ || RS  and   PS || QR.
    4. ∠SPQ = ∠QRS  and ∠PQR = ∠RSP

Note : Parallelogram is a Rectangle if and only if all angles right angle.

Note : Diagonals are bisect to each other in all case.

 

To Prove :

    1. Rectangle :

                         Opposite sides and diagonals are equal.

2. Square  :

                         All sides and diagonals are equal.

3. Rhombus :

                        All sides are equal and diagonals are not            equal.

4. Paralellogram :

                                 Opposite sides are equal and diagonals are not equal.

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