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Mathematics Class 7 - The Triangle-And-Its-Properties Notes

Comprehensive study notes for Class 7 - The Triangle-And-Its-Properties olympiad preparation

The Triangle and Its Properties

Welcome to the chapter on The Triangle and Its Properties for Class 7. In this chapter, you will learn about triangles, their types, properties, and important concepts like medians, altitudes, and the angle sum property. By the end of this chapter, you will be able to identify different triangles and use their properties to solve problems!

Introduction

A triangle is a closed figure with three sides, three angles, and three vertices. Triangles are one of the basic shapes in geometry and have many interesting properties.

Types of Triangles

  • Based on Sides:
    • Scalene Triangle: All sides are of different lengths.
    • Isosceles Triangle: Two sides are equal.
    • Equilateral Triangle: All three sides are equal.
  • Based on Angles:
    • Acute Triangle: All angles are less than 90°.
    • Right Triangle: One angle is exactly 90°.
    • Obtuse Triangle: One angle is more than 90°.

Properties of a Triangle

  • The sum of the lengths of any two sides is greater than the length of the third side.
  • The sum of the three angles of a triangle is always 180°.

Angle Sum Property

The sum of the angles in any triangle is always 180°. For example, if two angles are 50° and 60°, the third angle will be 70°.

Medians and Altitudes

  • Median: A line segment joining a vertex to the midpoint of the opposite side.
  • Altitude: A perpendicular line segment from a vertex to the opposite side (or its extension).

Exterior Angle Property

The measure of an exterior angle of a triangle is equal to the sum of the two opposite interior angles.

  • Example: If one exterior angle is 120°, and one opposite interior angle is 50°, the other opposite interior angle will be 70°.

Fun Activity: Triangle Hunt!

Look around your home or classroom and find objects shaped like triangles. Draw and label their sides and angles!

Summary

  • Triangles have three sides, three angles, and three vertices.
  • There are different types of triangles based on sides and angles.
  • The sum of the angles in a triangle is always 180°.
  • Medians and altitudes are important lines in a triangle.
  • The exterior angle property helps solve triangle problems.

Practice Questions

  1. Name the three types of triangles based on sides.
  2. What is the sum of the angles in a triangle?
  3. Draw a triangle and label its medians.
  4. If two angles of a triangle are 65° and 75°, what is the third angle?
  5. What is an exterior angle of a triangle?

Challenge Yourself

  • Find the type of triangle if its sides are 5 cm, 5 cm, and 8 cm.
  • Draw a right triangle and mark its right angle.

Did You Know?

  • Triangles are used in building bridges and towers because they are very strong shapes!
  • The Bermuda Triangle is a famous area in the ocean shaped like a triangle.

Glossary

  • Triangle: A shape with three sides and three angles.
  • Median: A line from a vertex to the midpoint of the opposite side.
  • Altitude: A perpendicular line from a vertex to the opposite side.
  • Exterior Angle: An angle formed outside the triangle when one side is extended.

Answers to Practice Questions

  1. Scalene, isosceles, equilateral.
  2. 180°.
  3. (Student should draw and label three medians.)
  4. 40° (because 180° - 65° - 75° = 40°).
  5. An exterior angle is formed when a side of a triangle is extended; it equals the sum of the two opposite interior angles.

Triangles are everywhere! Learn their properties and use them to solve geometry problems.

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