The Triangle and Its Properties
Medians, altitudes, exterior angle property, and triangle inequality.
Chapter Overview
Triangles have unique properties — angle sum 180°, exterior angle theorem, medians, altitudes, and triangle inequality. Essential for geometry through Class 10.
Angle Properties
Angle sum
∠A + ∠B + ∠C = 180°
Exterior angle
Exterior angle = sum of two opposite interior angles
Medians and Altitudes
- Median: vertex to midpoint of opposite side
- Altitude: perpendicular from vertex to opposite side
- Centroid divides medians in 2:1 ratio (introduced)
Triangle Inequality
Sum of any two sides > third side. This determines if three lengths can form a triangle.
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Find Third Angle
Two angles of a triangle are 55° and 65°. Find the third.
- 1Sum = 180°
- 2Third = 180° − 55° − 65°
Answer
60°
Example 2: Exterior Angle
In ΔABC, ∠A = 50°, ∠B = 70°. Find exterior angle at C.
- 1Exterior at C = ∠A + ∠B
Answer
120°
Key Points to Remember
- ✓ Equilateral triangle: each angle 60°
- ✓ Right triangle has one 90° angle
- ✓ Longest side opposite largest angle
Exam Tips
- • Use angle sum property first
- • State exterior angle theorem when used
Practice MCQs — The Triangle and Its Properties
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Sum of angles in a triangle is: