Topics
Patterns in Mathematics
- Mathematical Patterns
- Patterns in Numbers
- Patterns in Shapes
Mathematics
Lines and Angles
Number Play
- Fundamentals of Numbers
- Supercells
- Number Line
- Working with Number Digits
- Palindromic Patterns
- Kaprekar Number
- Clock and Calendar Numbers
- Mental Math
- Patterns in Numbers
- The Collatz Conjecture
- Basic Concept of Estimation and Approximation of Numbers
Data Handling and Presentation
- Mathematical Data Collection and Organisation
- Pictographs
- Bar Graphs
- Artistic and Aesthetic Considerations
Prime Time
- Multiples and Common Multiples
- Factors and Common Factors
- Prime and Composite Numbers
- Eratosthenes’ Method of Finding Prime Numbers
- Co-prime Numbers
- Prime Factorisation
- Tests for Divisibility of Numbers
- Divisibility by 10
- Divisibility by 5
- Divisibility by 2
- Divisibility by 4
- Divisibility by 8
- Exploring Special Numbers & Logical Reasoning
Perimeter and Area
- Concept of Perimeter
- Perimeter of a Rectangle
- Perimeter of Squares
- Perimeter of Triangle
- Problems based on Perimeter
- Perimeter of a Regular Polygon
- Perimeter of an Equilateral Triangle
- Concept of Area
- Problems based on Area
- Area of a Triangle
- Exploring Shapes Through Perimeter and Area
Fractions
Playing with Constructions
- Basic Concept of Construction
- Squares and Rectangles
- Constructing Squares and Rectangles
- An Exploration in Rectangles
- Constructing Complex Figures
- Exploring Diagonals of Rectangles and Squares
- Points Equidistant from Two Given Points
Symmetry
The Other Side of Zero
- Fundamentals of Numbers
- Negative and Positive Numbers
- Tracking Movement: Using Positive and Negative Numbers
- Comparison of Integers
- Number Line
- Conversion between Addition and Subtraction
- The Token Model
- Integers in Other Places
- Explorations with Integers
- Integers
- Definition
- Properties of an Angle Bisector
- Activity
Definition
If a line or line segment divides an angle into two equal angles, then the line or line segment is called the angle bisector of the given angle.
Properties of an Angle Bisector
Properties of an Angle Bisector:
- An angle bisector divides an angle into two equal parts.
- Any point on the bisector of an angle is equidistant from the sides or arms of the angle.
- A triangle divides the opposite side into the ratio of the measures of the other two sides.
Example:
OD is the angle bisector of ∠COA
QS is the angle bisector of ∠RQP
Activity
To Understand Angle Bisector:
Construction:
1. Draw an angle of any measure on a piece of tracing paper.
2. Fold the paper such that the two arms of the angle overlap exactly.
3. Unfold the paper and observe the crease formed — this feature is the angle bisector.
4. Mark two points, A and B, on the arms of the angle at equal distances from the vertex.
5. Mark points C, P, and T on the fold (angle bisector).
6. Measure the distances from each of these points (C, P, T) to points A and B.
Observation:
1. The fold (crease) divides the angle into two equal parts.
2. Points C, P, and T on the fold are equidistant from points A and B on the arms of the angle.
Conclusion:
1. The angle bisector divides the angle into two equal angles.
2. Any point on the angle bisector is equidistant from both arms of the angle.
