CHAPTER 6: THE TRIANGLE AND ITS PROPERTIES

What is a Triangle?

A triangle is a shape with 3 sides, 3 corners, and 3 angles. It's the strongest shape in nature!

Where do we see triangles?

• Roofs of houses (strong structure)

• Bridges and towers (strong support)

• Samosa and sandwich halves

• Traffic warning signs

• Mountains in the distance

Types of Triangles

By Sides:

1. Equilateral triangle - All sides equal

2. Isosceles triangle - Two sides equal

3. Scalene triangle - All sides different

By Angles:

1. Acute triangle - All angles < 90°

2. Right triangle - One angle = 90°

3. Obtuse triangle - One angle > 90°

Special Properties

Angle Sum Property:

All 3 angles of a triangle always add to 180°

If two angles are 60° and 70°

Third angle = 180° - (60° + 70°) = 50°

Pythagoras Theorem (for right triangles):

In a right triangle:

(Base)² + (Height)² = (Hypotenuse)²

Used in construction and measurement

What You Will Learn

In this chapter, we will learn:

  • Different types of triangles
  • Angle sum property of triangle
  • Exterior angle property
  • Triangle inequality property
  • Pythagoras theorem
  • Right angled triangles
  • Altitude and median of triangle

Why is it Important?

Triangles are important because:

  • They are the strongest shape for buildings
  • Used in bridge construction
  • Help in measuring heights and distances
  • Used in navigation and maps
  • Important for art and design
  • Used in computer graphics
  • Essential for engineering and architecture
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For Class 7 Students (NCERT & JKBOSE)