A Tale of Three Intersecting Lines

Overview

Three intersecting line segments can form a triangle. This chapter studies triangles, their angles and sides, and the important angle sum and exterior angle properties.

Key concepts

• A triangle has three sides, three vertices and three angles.
• Types by sides: equilateral, isosceles, scalene.
• Types by angles: acute, right, obtuse.
• The three angles of a triangle always add up to 180°.
• Triangle inequality: any two sides together exceed the third.

Important formulae

• Angle sum of a triangle = 180°
• Exterior angle = sum of two opposite interior angles
• Sum of any two sides > third side

Solved example

1. Two angles of a triangle are 50° and 60°. Find the third.
2. Sum of all angles = 180°.
3. Third angle = 180° − (50° + 60°) = 70°.

Important questions

1. Can a triangle have sides 3 cm, 4 cm and 8 cm? Why?
2. Find the exterior angle if the two opposite interior angles are 45° and 55°.
3. Classify a triangle with angles 90°, 45°, 45°.
4. What is each angle of an equilateral triangle?

Quick revision

The angles of every triangle add to 180°. An exterior angle equals the sum of the two far interior angles, and the triangle inequality decides if sides can form a triangle.