NCERT Class 8 Mathematics Chapter 3 Understanding Quadrilaterals CBSE Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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Understanding Quadrilaterals

Polygons

A simple closed curve made up of only line segments is called a polygon.

Simple Curve Polygons

Convex Polygon

We have all the diagonals inside the polygon

Convex Polygon

Concave Polygon

We don՚t have all the diagonals inside the Polygon

Concave Polygon

Regular and Irregular Polygons

A regular polygon is both ‘equiangular’ and ‘equilateral’

So all the sides and angles should be same

  • So square is regular polygon but rectangle is not
  • Equilateral triangle is a regular polygon

Angle Sum in the Polygons

The Sum of the angles in the polygon is given by

For Triangle,

So Total

For quadrilateral,

So Total

Classification of Polygons

We classify polygons according to the number of sides (or vertices)

Classification of Polygons
Number of sidesClassification
3Triangle
4Quadrilateral
5Pentagon
6Hexagon
7Heptagon
8Octagon
9Nonagon
Terms and Descriptions
S. noTermsDescriptions
1.QuadrilateralA quadrilateral is a four-sided polygon with four angles. There are many kinds of quadrilateral. The five most common types are the parallelogram, the rectangle, the square, the trapezoid, and the rhombus.
A Quadrilateral is a Four-Sided Polygon with Four Angles
2.Angle Property of quadrilateral
  • Sum of all the interior angles is
  • Sum of all the exterior angles is
3.parallelogramA quadrilateral which has both pairs of opposite sides parallel is called a parallelogram.

Its properties are:

  • The opposite sides of a parallelogram are equal.
  • The opposite angles of a parallelogram are equal
  • The diagonals of a parallelogram bisect each other.
  • The adjacent angles in a parallelogram are supplementary.
Called a Parallelogram
4.TrapeziumA quadrilateral which has one pair of opposite sides parallel is called a trapezium.
Called a Trapezium
5.KiteIt is a quadrilaterals having exactly two distinct consecutive pairs of sides of equal length

Here ABCD is a Kite

ABCD is a Kite

6.RhombusRhombus is a parallelogram in which any pair of adjacent sides is equal.

Properties of a rhombus:

  • All sides of a rhombus are equal
  • The opposite angles of a rhombus are equal
  • The diagonals of a rhombus bisect each other at right angles.
Rhombus is a Parallelogram
7.RectanglesA parallelogram which has one of its angles a right angle is called a rectangle.

Properties of a rectangle are:

  • The opposite sides of a rectangle are equal
  • Each angle of a rectangle is a right-angle.
  • The diagonals of a rectangle are equal.
  • The diagonals of a rectangle bisect each other.
Properties of a Rectangle
8.SquareA quadrilateral, all of whose sides are equal and all of whose angles are right angles.
  • Properties of Square are equal.
  • All the sides of a square are equal.
  • Each of the angles measures 900.

The diagonals of a square bisect each other at right angles. The diagonals of a square are equal.

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