CLASSIFY QUADRILATERALS

About "Classify quadrilaterals"

Classify quadrilaterals :

A closed geometric figure with four sides and four vertices is called a quadrilateral. The sum of all the four angles of a quadrilateral is 360°.

A quadrilateral can be classified as follows.

(i) Square 

(ii) Rectangle

(iii) Parallelogram

(iv) Rhombus

Square :

A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted ABCD.

Properties of square

  • All four sides of a square are same length, they are equal
  • Opposite side of a square are parallel
  • All four angles of a square are right angles
  • Sum of the angles of a square are equal to 360 degree.
  • Diagonals of a square are same length
  • Each diagonal of a square divides its into  two equal symmetrical area.
  • Diagonals of a square intersect its right angles, and share each other half.

Area of a square  =  a²

Perimeter of a square  =  4 a

Here "a" stands for side length of the square.

Rectangle :

A rectangle is a quadrilateral with four right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal.

Properties of rectangle

  • An opposite sides of a rectangle are the same length, they are equal
  • An opposite sides of a rectangle are parallel
  • An adjacent sides of a rectangle are always perpendicular
  • All four angles of a rectangles is right.
  • The sum all of the angles of a rectangle is equal to 360 degrees.
  • The diagonals of a rectangle are equal
  • The sum of squares two diagonals is equal to the sum of squares of the sides.

Area of the rectangle  =  length x width

Perimeter of the rectangle  =  2(length  + width)

Parallelogram :

A quadrilateral in which the opposite sides are parallel is called a parallelogram.

  • Opposite sides are parallel and equal.
  • Opposite angles are equal and sum of any two adjacent angles is 180°.
  • Diagonals bisect each other.
  • The sum of the parallelogram angles is equal to 360 degrees.
  • Each diagonals divides the parallelogram into two equal triangle.
  • Two diagonals is divided parallelogram into two pairs of equal triangles.

Area of parallelogram  =  base x height (or) 

Area of parallelogram  =  diagonal 1 x diagonals 2 

Perimeter of parallelogram  =  Sum of length of all sides

Rhombus :

A rhombus is a simple quadrilateral whose four sides all have the same length.

  • All sides are equal and opposite sides are parallel
  • Opposite angles are equal and sum of any two adjacent angles is 180°.
  • Diagonals bisect each other at right angles.
  • The intersecting point of the diagonals is the center of the symmetry.
  • At any rhombus can be inscribed a circle.

Area of rhombus  =  (1/2)(diagonal 1 x diagonals 2)

Perimeter of rhombus  =  Sum of length of all sides

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