Page 171 - Maths Skills - 8

Understanding Quadrilaterals 169

MIND MAP

Understanding Quadrilateral

Polygon Properties of Specific Quadrilateral
“A simple closed S. No. Properties Parallelogram Rectangle Square Rhombus
curve made up of
only line segment 1. Opposite sides are parallel. Yes Yes Yes Yes
is called a polygon” 2. Opposite sides are equal. Yes Yes Yes Yes
3. Adjacent sides are equal. No No Yes Yes
4. Opposite angles are equal. Yes Yes Yes Yes
5. All angles are right angle. No Yes Yes No
6. Diagonals are equal. No Yes Yes No

Types 7. Diagonals bisect each other. Yes Yes Yes Yes
8. Diagonals bisect at right angles. No No Yes Yes
9. Diagonals bisect interior angles No No Yes Yes

Concave Polygon
In this, atleast one angle is Convex Polygon Cyclic Quadrilateral
more than 180° In this, A
In this, each angle is ∠A + ∠C = 180°
less than 180° ∠B + ∠D = 180° B D

C
Properties

� Sum of all interior angles = (2n – 4) × 90°
where, n is the number of sides of
convex polygon Kite
� Sum of all exterior angles = 360° � Adjacent sides are equal D
n (n – 3) � Opposite sides are unequal 90°
� Number of Diagonals = � Diagonals are perpendicular A C
2
where, n = Number of sides of polygon � One diagonal is perpendicular B
bisector of the other