Types of Quadrilaterals

Topics

Number System(Consolidating the Sense of Numberness)
- Comparing Numbers
- To Form The Smallest and The Greatest Numbers Using Given Digits
- Operations on Larger Numbers
Number System
Estimation
- Basic Concept of Estimation and Approximation of Numbers
- Rounding off a Number
- Estimation in Basic Operations
Ratio and Proportion
Algebra
Numbers in India and International System (With Comparison)
- Concept of Unit, Number, Numeral and Numeration
- Hindu-Arabic (Indian) System of Numeration
- International System of Numeration
- Indian vs. International Place Value System
Geometry
Place Value
- Concept of Place Value
- Largest and Smallest Numbers
Mensuration
Natural Numbers and Whole Numbers (Including Patterns)
- Natural Numbers
- Whole Numbers
- Successor and Predecessor of Whole Number
- Properties of Whole Numbers
- Mathematical Patterns
- Patterns in Whole/Natural Numbers
- Magic Square
- Matchstick Pattern
Data Handling
Negative Numbers and Integers
- Concept of Negative Numbers
- Integers
- Ordering of Integers
- Addition of Integers
- Subtraction of Integers
- Integers
Number Line
- Number Line
- Representation of Natural numbers, Whole Numbers and Integers On Number Line
- Comparing Numbers
- Addition and Subtraction on a Number Line
HCF and LCM
- Factors and Common Factors
- Prime and Composite Numbers
- Eratosthenes’ Method of Finding Prime Numbers
- Prime Factorisation
- Highest Common Factor (HCF)
- Methods of Finding HCF
- Multiples and Common Multiples
- Lowest Common Multiple
- Methods of Finding LCM
Playing with Numbers
- Simplification of Brackets
- Finding Factors Using Rectangular Arrangements and Division
- Factors and Common Factors
- Multiples and Common Multiples
- Concept of Even and Odd Number
- Tests for Divisibility of Numbers
- Divisibility by 2
- Divisibility by 4
- Divisibility by 8
- Divisibility by 3
- Divisibility by 6
- Divisibility by 9
- Divisibility by 5
- Divisibility by 11
Sets
- Concept of Sets
- Representation of a Set
- Types of Sets
- Cardinality of a Set
Ratio
- Quantitative Comparison Using Basic Operations
- Ratio
- Simplifying Ratios
- Problems based on Ratio
- All About Ratios: Dividing, Comparing, and Modifying Quantities
Proportion (Including Word Problems)
- Proportion
- Concept of Continued Proportion
Unitary Method
- Unitary Method
- Types of Variation
Fractions
- Concept of Fraction
- Types of Fractions
- Concept of Proper and Improper Fractions
- Concept of Mixed Fractions
- Like and Unlike Fraction
- Concept of Equivalent Fractions
- Conversion between Improper and Mixed fraction
- Conversion between Unlike and Like Fractions
- Simplest Form of a Fractions
- Comparing Fractions
- Addition of Fraction
- Subtraction of Fraction
- Multiplication of Fraction
- Division of Fractions
- Using Operator 'Of' with Multiplication and Division
- BODMAS Rule
- Problems Based on Fraction
Decimal Fractions
- Like and Unlike Decimal Numbers
- The Decimal Number System
- Conversion between Decimal Fraction and Common Fraction
- Addition of Decimal Fraction
- Subtraction of Decimal Numbers
- Multiplication of Decimal Numbers
- Division of Decimal Numbers
- Application of Decimals in Real Life
- Word Problems based on Decimals
Percent (Percentage)
- Basic Concept of Percentage
- Conversion between Percentage and Fraction or Decimal
- Expressing Quantities as Percentages
- Increase or Decrease in Percent
- Percentage Problems Related to Environment
Idea of Speed, Distance and Time
- Speed, Distance and Time
- Uniform Speed, Variable Speed, and Conversions
Fundamental Concepts
- Introduction to Algebra
- Constants and Variables in Mathematics
- Classification of Terms in Algebra
- Algebraic Expressions
- Factors and Common Factors
- Powers and Exponents
- Basic Concept of Polynomial and its Degree
Fundamental Operations (Related to Algebraic Expressions)
- Addition of Like and Unlike Terms
- Subtraction of Like and Unlike Terms
- Addition of Polynomials
- Subtraction of Polynomials
- Multiplication of Algebraic Expressions
- Division of Algebraic Expressions
Substitution (Including Use of Brackets as Grouping Symbols)
- Basic Concept of Substitution
- Brackets in Mathematics
Framing Algebraic Expressions (Including Evaluation)
- Algebraic Expressions
- Evaluation of Algebraic Expressions
Simple (Linear) Equations (Including Word Problems)
- Concept of Linear Equations
- Rules for Solving a Linear Equation
- Methods of Solving Linear Equations
- Word Problems on Linear Equations
Fundamental Concepts
- Fundamentals of Geometrical Concepts
- Concept of Points
- Concept of Lines
- Rays
- Line Segments
- Mathematical Concept of Surface
- Planes
- Parallel Lines
- Intersecting Lines
- Concept for Open and Closed Figures
- Plane Closed Figures
- The Perpendicular
- The Perpendicular Bisector
Angles (With Their Types)
- Concept of Angle
- Angle and Its Formation
- Measuring Angles
- Types of Angles
- Concept of Pairs of Angles
- The Sum of the Angles Around a Point is Always 360°
Properties of Angles and Lines (Including Parallel Lines)
- Properties of Adjacent and Vertically Opposite Angles
- Parallel Lines
- Concept of Transversal Lines
- Construction of an Angle
- Drawing a Perpendicular to a Line
Triangles (Including Types, Properties and Constructions)
- Basic Concepts of Triangles
- Exterior Angle of a Triangle and Its Property
- Classification of Triangles based on Angles
- Classification of Triangles based on Sides
- Altitudes of a Triangle
- Median of a Triangle
- Construction of Triangles
Quadrilateral
- Quadrilaterals
- Angle sum Property of Quadrilateral
- Types of Quadrilaterals
Polygons
- Basic Concept of Polygons
- Sum of Interior Angles of a Polygon
- Sum of Exterior Angles of a Polygon
- Basic Concept of Regular Polygon
The Circle
- Basic Concept of Circle
- Secant and Tangent
- Arc of the Circle
- Sector of a Circle
- Segment of a Circle
- The Interior and the Exterior of a Circle
- Circumcircle of a Triangle
- Incircle of a Triangle
Symmetry (Including Constructions on Symmetry)
- Concept of Symmetry
- Reflection Symmetry in 2-D Shapes
- Construction of Symmetric Points and Lines
Recognition of Solids
- Identification of 3-d Shapes
- Faces, Edges and Vertices of Polyhedron
- Nets of 3D Figures
- Oblique Sketches of 3D Shapes
Perimeter and Area of Plane Figures
- Basic Concepts in Mensuration
- Concept of Perimeter
- Perimeter of a Rectangle
- Perimeter of Squares
- Perimeter of an Equilateral Triangle
- Problems based on Perimeter
- Shapes with the Same Perimeter
- Concept of Area
- Area of Rectangle
- Area of Square
- Problems based on Area
Data Handling (Including Pictograph and Bar Graph)
- Mathematical Data Collection and Organisation
- Frequency Distribution and Its Applications
- Pictographs
- Bar Graphs
Mean and Median
- Concept of Mean (Average)
- Basic Concept of Median

Estimated time: 24 minutes

Introduction
Trapezium
Isosceles Trapezium
Parallelogram
Rectangle
Rhombus
Square
Example 1
Example 2
Example 3
Key Points Summary

CISCE: Class 6

Introduction

A quadrilateral is a closed figure with four sides and four angles. Based on the relationships between its sides and angles, different types of quadrilaterals exist — such as trapezium, parallelogram, rectangle, rhombus, and square.

Understanding these shapes is essential because they form the basis for most of the structures and objects we encounter daily, from rectangles and squares to the less common parallelograms and trapeziums.

CISCE: Class 6

Trapezium

Has only ONE pair of parallel sides then ABCD is a trapezium.

Key Properties:

Sum of angles = 360°
Co-interior angles = 180° (angles on the same side of parallel lines ∠A + ∠D = 180° and ∠B + ∠C = 180°)

CISCE: Class 6

Isosceles Trapezium

Non-parallel sides are equal is called an isosceles trapezium.

Key Properties:

Non-parallel sides are equal:

Base angles are equal:
The diagonals are equal in length:
The pairs of co-interior angles are supplementary:

CISCE: Class 6

Parallelogram

Has TWO pairs of parallel sides (opposite sides face each other)

Key Properties:

Opposite sides are equal in length
AB = DC and AD = BC
Opposite angles are equal
∠A = ∠C and ∠B = ∠D
Adjacent angles add up to 180°
∠A + ∠B = 180° and ∠B + ∠C = 180°
∠C + ∠D = 180° and ∠D+ ∠A= 180°
Diagonals bisect each other (cross at their midpoints)
OA = OC and OB = OD

CISCE: Class 6

Rectangle

ALL FOUR angles are 90°

Key Properties:

All angles = 90°
Opposite sides are equal
AB = DC,AD = BC
Opposite sides are parallel
Diagonals are equal in length
AC = BD
Diagonals bisect each other
OA = OC,OB = OD

CISCE: Class 6

Rhombus

A rhombus is a quadrilateral in which ALL SIDES are equal.

Key Properties:

All sides are equal
Opposite angles are equal.
Diagonals bisect each other at right angles (90°).
A parallelogram with equal adjacent sides.

CISCE: Class 6

Square

A square is a quadrilateral in which ALL SIDES are equal and each angle is 90°.

Key Properties:

All sides are equal
All angles are right angles
Diagonals are equal and bisect each other at right angles.

CISCE: Class 6

Example 1

Isosceles trapezium ABCD with ∠B 82°. find angles A, C and D.

Solution:
Steps:

∠A = ∠B = 82° (Base angles are equal)
∠C + ∠B = 180° => ∠C + 82° = 180° (Co-interior (same-side) angles on parallel lines are 180∘)
∠C = 180° − 82° = 98°
∠D = ∠C = 98°
∴ ∠A = 82°, ∠C = 98° and ∠D = 98°.

CISCE: Class 6

Example 2

Each angle of a quadrilateral equals x. Show it’s a rectangle.

Solution:
Steps:

Sum of interior angles of any quadrilateral $= 36 0 \circ$ .
$x + x + x + x = 4 x = 36 0 \circ$ .

Conclusion: and the figure is a rectangle.

CISCE: Class 6

Example 3

Rhombus ABCD, with a diagonal = AC and ∠ DAC = 30°. Find all the angles of the rhombus.

Solution:
Steps:

∴ ∠CAB = ∠DAC = 30° (diagonals bisect the angles at the vertex.)
==> ∠DAB = 30° + 30° = 60°
∠BCD = ∠DAB = 60° (opposite angles are equal.)
∠DAB + ∠ABC = 180° (adjacent angles are supplementary).
⇒ 60° + ∠ABC = 180°
∠ABC = 180° − 60 = 120°
Also, ∠ADC = ∠ABC = 120°
∴ Required angles are 60°, 120°, 60° and 120°

CISCE: Class 6

Key Points Summary

Quadrilateral	Parallel Sides	Sides Equal	Angles	Diagonals
Trapezium	One pair	Not equal	Co-interior angles = 180°	Not equal, don’t bisect
Isosceles Trapezium	One pair	Non-parallel sides equal	Base angles equal	Equal in length
Parallelogram	Two pairs	Opposite sides equal	Opposite angles equal	Bisect each other
Rectangle	Two pairs	Opposite sides equal	All 90°	Equal and bisect each other
Rhombus	Two pairs	All sides equal	Opposite angles equal	Bisect at 90°
Square	Two pairs	All sides equal	All 90°	Equal and bisect at 90°

Test Yourself

Class 6 MCQ Test

Types of Quadrilaterals

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Topics

Number System(Consolidating the Sense of Numberness)

Number System

Estimation

Ratio and Proportion

Algebra

Numbers in India and International System (With Comparison)

Geometry

Place Value

Mensuration

Natural Numbers and Whole Numbers (Including Patterns)

Data Handling

Negative Numbers and Integers

Number Line

HCF and LCM

Playing with Numbers

Sets

Ratio

Proportion (Including Word Problems)

Unitary Method

Fractions

Decimal Fractions

Percent (Percentage)

Idea of Speed, Distance and Time

Fundamental Concepts

Fundamental Operations (Related to Algebraic Expressions)

Substitution (Including Use of Brackets as Grouping Symbols)

Framing Algebraic Expressions (Including Evaluation)

Simple (Linear) Equations (Including Word Problems)

Fundamental Concepts

Angles (With Their Types)

Properties of Angles and Lines (Including Parallel Lines)

Triangles (Including Types, Properties and Constructions)

Quadrilateral

Polygons

The Circle

Symmetry (Including Constructions on Symmetry)

Recognition of Solids

Perimeter and Area of Plane Figures

Data Handling (Including Pictograph and Bar Graph)

Mean and Median

Introduction

Trapezium

Isosceles Trapezium

Parallelogram

Rectangle

Rhombus

Square

Example 1

Example 2

Example 3

Key Points Summary

Test Yourself

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