Notes Maths Class 7 Chapter 7 Ganita Prakash

Notes For All Chapters – Ganita Prakash Class 7th

A Tale of Three Intersecting Lines

1. Triangle and its Parts

A triangle has 3 sides, 3 vertices, and 3 angles.

Example: Triangle ABC has angles ∠A, ∠B, ∠C.

2. Types of Triangles by Sides

Type Description
Equilateral All 3 sides equal
Isosceles 2 sides equal
Scalene All 3 sides different

3. Triangle Construction Methods

A. When all 3 sides are given

• Use compass to draw arcs from the endpoints of the base.
• The point where arcs meet is the third vertex.

B. When two sides and the included angle are given

• Draw one side as base.
• Use protractor to draw given angle.
• Use ruler to mark the second side.

C. When two angles and the included side are given

• Draw the base side.
• Use protractor to draw two angles at both ends.
• Extend both arms — the intersection is the third vertex.

4. Triangle Inequality Rule

A triangle can exist only if the sum of any two sides is greater than the third side.

Example:

Triangle possible: 3 cm, 4 cm, 5 cm → ✅

Triangle not possible: 3 cm, 4 cm, 9 cm → ❌

5. Angle Sum Property

The sum of all 3 angles in any triangle is always 180°.

∠A + ∠B + ∠C = 180°

6. Altitudes of Triangle

Altitude: A perpendicular drawn from a vertex to the opposite side (or its extension).

Every triangle has 3 altitudes.

7. Exterior Angle Property

Exterior angle = Sum of the two opposite interior angles.

∠Exterior = ∠Interior1 + ∠Interior2

8. Triangles by Angles

9. Key Constructions to Practice

Equilateral triangle (e.g., 4 cm sides)

Triangle with sides 4 cm, 5 cm, 6 cm

Triangle with 2 sides and 1 included angle (e.g., 5 cm, 4 cm, ∠A = 45°)

Triangle with 2 angles and 1 side (e.g., ∠A = 45°, ∠B = 80°, AB = 5 cm)

Construct altitudes from a vertex to the base