1. Mathematics - Class 8 Chapter 3 Unit 5
QUADRILATERALS
Mathematics - Class 8
Chapter 3 Unit 5

2. Module Objectives Learn to identify quadrilaterals
Understand basic properties of quadrilaterals
Classify quadrilaterals into common types, and recognize their specific properties

3. Basic Geometrical Figures
Line
Bounded by 2 end points
All points are collinear i.e. lie on the
same straight line
Triangle
Plane figure bounded by three sides
Atleast 3 non-collinear points
Quadrilateral
‘Quad’ = four, ‘lateral’ = side
Formed by joining 4 points
Any 3 out of these 4 points are non-collinear

4. Quadrilaterals
Any closed figure having four sides formed by joining four points and three of which are not collinear is called quadrilateral. A C B D W Y Z X P Q R S M O P N

5. Are these Quadrilaterals?B C D A B C D
No, the sides cross each other
No, the sides are all not line segments
Yes, it is a closed figure
formed by the union of four line segments
that join 4 points lying on the same plane
no three of which are collinear
and each segment meet exactly 2 other lines, each at their end point A C B D

6. Quadrilateral Notations
Let ABCD be a quadrilateral
Vertices - Points A, B, C and D
Four sides - Segments AB, BC, CD and DA
Four angles - DAB, ABC, BCD and CDA
Two diagonals - Segments AC and BD A C B D
Naming a quadrilateral e.g. ABCD
Refer to its vertices in a particular order
We cannot read it as ADBC or ADCB
Naming Hint: If you join adjacent letters in the name, then there should not be any crossing of line segments

7. Quadrilateral Notations
Adjacent or consecutive sides
Two sides of a quadrilateral have a common end point
E.g. AB and AD, CD and CB
Opposite sides
Two sides do NOT have a common end point
E.g. AB and DC A C B D

8. Quadrilateral Notations
Adjacent or consecutive angles
Two angles have a side common to them
E.g. DAB and ABC, with AB being the common side
Opposite angles
Two angles do NOT have a common side
E.g. DAB and ABC A C B D

9. Properties of Quadrilaterals
Diagonal Property
Diagonal AC divides the quadrilateral into 2 triangles ABC and ADC
Angle Sum Property
The sum of the angles of a quadrilateral is 360.
ABC + BCD + CDA + DAB = 360 A C B A D B C

10. Types of Quadrilaterals
Convex Quadrilateral
Quadrilateral in which every internal angle of the quadrilateral is lesser than 180.
Concave Quadrilateral
A quadrilateral is concave if any internal angle of the quadrilateral is greater than 180. P Q R S N L M K

11. Special Kinds of Quadrilaterals
Classification based on nature of sides or angles
Type of Quadrilateral
Properties
Trapezium
One pair of opposite sides are parallel
Parallelogram
Both pairs of opposite sides are parallel
Opposite sides are equal and opposite angles are equal
Kite
Two pairs of equal-length adjacent sides
Is Parallelogram a type of Trapezium?
Yes, it has parallel opposite sides
Is Kite a type of Parallelogram?
No, it does not have 2 pairs of equal-length opposite sides

12. Trapezium Quadrilateral with a pair of opposite side that are parallel
Isoceles Trapezium
Non-parallel sides are equal
Base angles are equal
Diagonal are equals
Adjacent angles corresponding to parallel sides are supplementary

13. Parallelograms Both pairs of opposite sides are parallel
Opposite sides are of equal length
Special Kinds of Parallelograms
Rectangles
Rhombus
Square W Y Z X

14. Kinds of Parallelograms - Rectangle
All angles are equal and right angles
All sides are not equal
Diagonals are equal and bisect each other ά ά ά ά ά ά ά ά

15. Kinds of Parallelograms - Rhombus
All sides are equal
All angles are not equal
Diagonals bisect each other at right angles
Two diagonals divide the rhombus into four congruent right angled triangles
Angles are bisected by the diagonals D C B A

16. Kinds of Parallelograms - Square
All its angles are equal and right angles
All sides are equal
Both diagonals are equal
Diagonals bisect each other at right angles

17. Kind of Parallelograms
Parallel Sides
All Sides
All Angles
Diagonals
Rectangle
2 pairs of opposite sides
Equal
Equal &
Right angles
Bisect each other
Rhombus
Not equal
Bisect each other at right angles
Square

18. Kite Type of quadrilateral but not a parallelogram
Has 2 pairs of equal-length adjacent sides
Two isoceles triangles are joined along the common base
Rhombus is a special kind of Kite B D O C