Parallel and Intersecting Lines

Overview

This chapter studies how lines relate to each other. Lines may intersect at a point or stay parallel forever. We explore the angles formed when lines meet or are crossed by a transversal.

Key concepts

• Intersecting lines meet at exactly one point.
• Parallel lines never meet and are always the same distance apart.
• A transversal cuts two or more lines.
• Angle pairs: vertically opposite, corresponding, alternate, co-interior.

Important formulae

• Vertically opposite angles are equal.
• For parallel lines: corresponding angles are equal; alternate angles are equal.
• Co-interior angles add up to 180°.

Solved example

1. Two lines intersect making one angle 70°. Find the vertically opposite angle.
2. Vertically opposite angles are equal.
3. So the opposite angle = 70°.

Important questions

1. If two parallel lines are cut by a transversal and one corresponding angle is 110°, find its pair.
2. What is the sum of two co-interior angles?
3. Draw two intersecting lines and mark all four angles when one is 50°.
4. Name one real-life example of parallel lines.

Quick revision

Vertically opposite angles are always equal. When parallel lines meet a transversal, corresponding and alternate angles are equal, and co-interior angles sum to 180°.