Class 9 Maths Q1 to 4 | Ex 7.2 Chapter 7 | Triangles | CBSE NCERT | Session 2024-25

Introduction

This tutorial provides a step-by-step guide to solving questions 1 to 4 from Exercise 7.2 in Chapter 7 of Class 9 Maths, focusing on the topic of Triangles as per the CBSE NCERT syllabus for the 2024-25 academic session. This exercise emphasizes understanding the properties of triangles and applying them to solve various mathematical problems.

Step 1: Understand the Basics of Triangles

Before diving into the questions, ensure you are familiar with the fundamental concepts of triangles:

• Types of Triangles:
  • Equilateral (all sides equal).
  • Isosceles (two sides equal).
  • Scalene (all sides different).
• Triangle Properties:
  • The sum of the interior angles is always 180 degrees.
  • The length of any two sides must be greater than the length of the third side.

Step 2: Analyze Question 1

• Question 1: Determine if the given triangle can exist based on the lengths of its sides.
• Approach:
  1. Identify the lengths provided.
  2. Apply the triangle inequality theorem:
     • Check if the sum of any two sides is greater than the third side.
  3. Conclude whether the triangle can exist or not based on your findings.

Step 3: Solve Question 2

• Question 2: Find the missing angle in a triangle given the other two angles.
• Approach:
  1. Use the property that the sum of angles in a triangle is 180 degrees.
  2. Subtract the sum of the known angles from 180 to find the missing angle.
  3. Example:
     • If angles are 50° and 60°, then:

     Missing Angle = 180 - (50 + 60) = 70°
     

Step 4: Tackle Question 3

• Question 3: Determine if a triangle is valid based on specific angle measures.
• Approach:
  1. Check if the given angles sum up to 180 degrees.
  2. If they do, the triangle is valid; if not, it cannot exist.
  3. Example:
     • Angles of 70°, 50°, and 60°:

     70 + 50 + 60 = 180 (Valid Triangle)
     

Step 5: Complete Question 4

• Question 4: Classify the triangle based on its angles and sides.
• Approach:
  1. Use the angle measures to classify:
     • Acute (all angles < 90°).
     • Right (one angle = 90°).
     • Obtuse (one angle > 90°).
  2. Use side lengths to classify:
     • Equilateral, Isosceles, or Scalene.
  3. Present your classification clearly.

Conclusion

In this tutorial, you learned how to solve the first four questions of Exercise 7.2 on triangles in Class 9 Maths. Understanding the properties of triangles, applying the triangle inequality theorem, and utilizing angle sum properties are crucial for solving these types of problems. As a next step, practice additional questions from the exercise to reinforce your understanding and mastery of triangle concepts.