Topics
Integers
- Natural Numbers
- Whole Numbers
- Negative and Positive Numbers
- Integers
- Representation of Integers on the Number Line
- Ordering of Integers
- Addition of Integers
- Subtraction of Integers
- Properties of Addition and Subtraction of Integers
- Multiplication of a Positive and a Negative Integers
- Multiplication of Two Negative Integers
- Product of Three Or More Negative Integers
- Closure Property of Multiplication of Integers
- Commutative Property of Multiplication of Integers
- Multiplication of Integers with Zero
- Multiplicative Identity of Integers
- Associative Property of Multiplication of Integers
- Distributive Property of Multiplication of Integers
- Making Multiplication Easier of Integers
- Division of Integers
- Properties of Division of Integers
Fractions and Decimals
- Concept of Fraction
- Types of Fractions
- Concept of Proper and Improper Fractions
- Concept of Mixed Fractions
- Concept of Equivalent Fractions
- Like and Unlike Fraction
- Comparing Fractions
- Addition of Fraction
- Subtraction of Fraction
- Multiplication of a Fraction by a Whole Number
- Using Operator 'Of' with Multiplication and Division
- Multiplication of Fraction
- Division of Fractions
- Concept of Reciprocals or Multiplicative Inverses
- Problems Based on Fraction
- The Decimal Number System
- Comparing Decimal Numbers
- Addition of Decimal Fraction
- Subtraction of Decimal Numbers
- Multiplication of Decimal Numbers
- Division of Decimal Numbers
- Problems Based on Decimal Numbers
Data Handling
Simple Equations
Lines and Angles
The Triangle and Its Properties
- Basic Concepts of Triangles
- Classification of Triangles based on Sides
- Classification of Triangles based on Angles
- Median of a Triangle
- Altitudes of a Triangle
- Exterior Angle of a Triangle and Its Property
- Some Special Types of Triangles - Equilateral and Isosceles Triangles
- Basic Properties of a Triangle
- Right-angled Triangles and Pythagoras Property
Comparing Quantities
- Ratio
- Concept of Equivalent Ratios
- Proportion
- Unitary Method
- Basic Concept of Percentage
- Estimation in Percentages
- Interpreting Percentages
- Conversion between Percentage and Fraction or Decimal
- Ratios to Percents
- Increase Or Decrease as Percent
- Basic Concepts of Profit and Loss
- Profit or Loss as a Percentage
- Calculation of Interest
Congruence of Triangles
- Similarity and Congruency of Figures
- Congruence Among Line Segments
- Congruence of Angles
- Congruence of Triangles
- Criteria for Congruence of Triangles
- Criteria for Similarity of Triangles
- SAS Congruence Criterion
- ASA Congruence Criterion
- RHS Congruence Criterion
- Exceptional Criteria for Congruence of Triangles
Rational Numbers
- Rational Numbers
- Equivalent Rational Number
- Positive and Negative Rational Numbers
- Rational Numbers on a Number Line
- Rational Numbers in Standard Form
- Comparison of Rational Numbers
- Rational Numbers Between Two Rational Numbers
- Addition of Rational Number
- Subtraction of Rational Number
- Multiplication of Rational Numbers
- Division of Rational Numbers
Perimeter and Area
- Basic Concepts in Mensuration
- Concept of Perimeter
- Perimeter of a Rectangle
- Perimeter of Squares
- Perimeter of Triangle
- Perimeter of Polygon
- Concept of Area
- Area of Square
- Area of Rectangle
- Triangles as Parts of Rectangles and Square
- Generalising for Other Congruent Parts of Rectangles
- Area of a Parallelogram
- Area of a Triangle
- Circumference of a Circle
- Area of Circle
- Conversion of Units
- Problems based on Perimeter
- Problems based on Area
Practical Geometry
- Construction of a Line Parallel to a Given Line, Through a Point Not on the Line
- Construction of Triangles
- Constructing a Triangle When the Length of Its Three Sides Are Known (SSS Criterion)
- Constructing a Triangle When the Lengths of Two Sides and the Measure of the Angle Between Them Are Known. (SAS Criterion)
- Constructing a Triangle When the Measures of Two of Its Angles and the Length of the Side Included Between Them is Given. (ASA Criterion)
- Constructing a Right-angled Triangle When the Length of One Leg and Its Hypotenuse Are Given (RHS Criterion)
Algebraic Expressions
Exponents and Powers
- Concept of Exponents
- Multiplying Powers with the Same Base
- Dividing Powers with the Same Base
- Taking Power of a Power
- Multiplying Powers with Different Base and Same Exponents
- Dividing Powers with Different Base and Same Exponents
- Numbers with Exponent Zero, One, Negative Exponents
- Miscellaneous Examples Using the Laws of Exponents
- Decimal Number System Using Exponents and Powers
- Crores
Symmetry
Visualizing Solid Shapes
Estimated time: 14 minutes
- Definition: Exterior Angle
- Properties of Exterior Angles
- Example
- Key Points Summary
CISCE: Class 6
Definition: Exterior Angle
An exterior angle is formed when a side of a triangle is extended beyond its vertex. The angle created between the extended side and the adjacent side of the triangle is the exterior angle.
CISCE: Class 6
Properties of Exterior Angles
1. Supplementary to Adjacent Interior Angle
- Rule: An exterior angle is always adjacent and supplementary to its interior angle.
- Formula: Exterior Angle + Interior Angle = 180°
Example:
∠ACD + ∠ACB= 180°.
2. Equal to the Sum of Opposite Interior Angles
- Rule: The measure of an exterior angle is equal to the sum of its two interior opposite angles.
- Formula: Exterior Angle = Sum of the two Interior Opposite Angles
Example:
∠ABD = ∠A + ∠C
3. Six Exterior Angles in a Triangle
- Rule: When all sides of a triangle are extended in both directions, six exterior angles are formed
Example:
CISCE: Class 6
Example
| Exterior Angle | Adjacent Interior Angle | Interior Opposite Angles | The relation between an exterior angle and its adjacent interior angle | The relation between an exterior angle and the interior opposite angles |
| ∠1 | ∠A | ∠B and ∠C | ∠1 + ∠A = 180° | ∠1 = ∠B + ∠C |
| ∠2 | ∠A | ∠B and ∠C | ∠2 + ∠A = 180° | ∠2 = ∠B + ∠C |
| ∠3 | ∠B | ∠A and ∠C | ∠3 + ∠B = 180° | ∠3 = ∠A + ∠C |
| ∠4 | ∠B | ∠A and ∠C | ∠4 + ∠B = 180° | ∠4 = ∠A +∠C |
| ∠5 | ∠C | ∠A and ∠C | ∠5 + ∠C = 180° | ∠5 = ∠A + ∠B |
| ∠6 | ∠C | ∠A and ∠C | ∠6 + ∠C = 180° | ∠6 = ∠A + ∠B |
CISCE: Class 6
Key Points Summary
-
An exterior angle is formed by extending a side of a triangle.
-
It is supplementary to its adjacent interior angle.
-
It is equal to the sum of the two opposite interior angles.
-
A triangle has six exterior angles when all sides are extended.
TIp:
Whenever you see a triangle with a side extended, first check if the angle is adjacent (supplementary) or opposite (equal to sum). That tells you which property to use!
Example Question 1
Find angle x in Fig
Sum of interior opposite angles = Exterior angle
or 50° + x = 110°
or x = 60°
Test Yourself
Shaalaa.com | Exterior angle of a triangle Property
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Series: Exterior Angle of a Triangle
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