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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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