Class 7 Mathematics
Chapter 6: The Triangle and Its Properties
STAGE 0: Foundation
A triangle is a closed figure formed by three line segments. Triangles are the most basic shapes in geometry and are very strong structures.
Examples in daily life:
- Traffic signs
- Roof supports
- Bridges
STAGE 1: Parts of a Triangle
- Sides: Three line segments
- Vertices: Three corner points
- Angles: Three angles
The sum of the lengths of any two sides of a triangle is always greater than the third side.
STAGE 2: Types of Triangles (Based on Sides)
- Scalene Triangle: All sides are unequal
- Isosceles Triangle: Two sides are equal
- Equilateral Triangle: All sides are equal
STAGE 3: Types of Triangles (Based on Angles)
- Acute-angled Triangle: All angles less than 90°
- Right-angled Triangle: One angle is 90°
- Obtuse-angled Triangle: One angle greater than 90°
STAGE 4: Angle Sum Property of a Triangle
The sum of the three interior angles of a triangle is always 180°.
Example:
If two angles are 50° and 60°, the third angle is:
180° − (50° + 60°) = 70°
STAGE 5: Exterior Angle Property
The exterior angle of a triangle is equal to the sum of the two interior opposite angles.
Example:
If interior opposite angles are 40° and 50°,
Exterior angle = 40° + 50° = 90°
STAGE 6: Practice Questions
1. Define a triangle.
2. Name the three types of triangles based on sides.
3. What is the sum of angles of a triangle?
4. Find the third angle if two angles are 35° and 65°.
5. What is the exterior angle property?
Shaktimatha CBSE Learning
Class 7 Mathematics – Chapter 6: The Triangle and Its Properties
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