Mathematics · Class 9
Triangles
Congruence rules, inequalities, and properties of triangles.
3 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Triangles are three-sided polygons. Class 9 focuses on congruence criteria, properties of isosceles triangles, inequalities, and basic theorems used in geometric proofs.
Congruence Criteria
- SSS: three sides equal
- SAS: two sides and included angle equal
- ASA: two angles and included side equal
- RHS: right angle, hypotenuse, and one side equal
Properties
- Angles opposite equal sides in isosceles triangle are equal
- Sides opposite equal angles are equal
- Sum of any two sides > third side (triangle inequality)
- Exterior angle = sum of two opposite interior angles
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Isosceles triangle
In ΔABC, AB = AC and ∠B = 50°. Find ∠A.
- 1AB = AC → ∠B = ∠C = 50°
- 2Angle sum: ∠A = 180° − 50° − 50°
Answer
∠A = 80°
Example 2: Triangle inequality
Can sides 3 cm, 4 cm, 8 cm form a triangle?
- 13 + 4 = 7 < 8
- 2Sum of two smaller sides not greater than third
Answer
No, triangle cannot be formed
Key Points to Remember
- ✓ Congruent triangles have all corresponding parts equal
- ✓ Order of letters matters in congruence notation
- ✓ CPCT: corresponding parts of congruent triangles
Exam Tips
- • State congruence criterion clearly
- • Draw accurate diagrams with markings
- • Use CPCT after proving congruence
Practice MCQs — Triangles
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Sum of angles in a triangle is: