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.
Convex Polygon
We have all the diagonals inside the polygon
Concave Polygon
We don՚t have all the diagonals inside the 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)
Number of sides  Classification 
3  Triangle 
4  Quadrilateral 
5  Pentagon 
6  Hexagon 
7  Heptagon 
8  Octagon 
9  Nonagon 
S. no  Terms  Descriptions 
1.  Quadrilateral  A quadrilateral is a foursided 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. 
2.  Angle Property of quadrilateral 

3.  parallelogram  A quadrilateral which has both pairs of opposite sides parallel is called a parallelogram. Its properties are:

4.  Trapezium  A quadrilateral which has one pair of opposite sides parallel is called a trapezium. 
5.  Kite  It is a quadrilaterals having exactly two distinct consecutive pairs of sides of equal length Here ABCD is a Kite 
6.  Rhombus  Rhombus is a parallelogram in which any pair of adjacent sides is equal. Properties of a rhombus:

7.  Rectangles  A parallelogram which has one of its angles a right angle is called a rectangle. Properties of a rectangle are:

8.  Square  A quadrilateral, all of whose sides are equal and all of whose angles are right angles.
The diagonals of a square bisect each other at right angles. The diagonals of a square are equal. 