Lines, Segments, Parallel and Perpendicular

What you will learn

• Tell a line, a ray and a line segment apart.
• Say what parallel, perpendicular and intersecting lines are.
• Find these lines in shapes and objects.

Before you start: you should know the names of simple shapes. See Shapes All Around.

The idea

In maths a line is perfectly straight and goes on forever in both directions. We draw only part of it, with arrows at the ends. A ray starts at one point and goes on forever one way. A line segment is a piece of a line with two end points. The edge of a ruler is a segment.

Parallel, perpendicular and intersecting

Two lines in the same flat space can be related in three ways.

• Parallel lines never meet. They stay the same distance apart. We mark them with matching arrows.
• Perpendicular lines meet at a right angle, $90^\circ$. We mark the corner with a small square.
• Intersecting lines cross at a point, at any angle.

In the world

Look for lines everywhere. The edges of a book have both parallel and perpendicular pairs.

Worked examples

Example 1: In a rectangle

How many pairs of parallel and perpendicular sides does a rectangle have?

1. Opposite sides are parallel: two pairs.
2. Each corner is a right angle, so neighbouring sides are perpendicular.

Answer: $2$ pairs of parallel sides, and every pair of neighbouring sides is perpendicular.

Example 2: Name the line

A torch shines a beam from a point and the beam never stops. What is it?

1. It has one end point (the torch).
2. It goes on forever one way.

Answer: a ray

Example 3: The letter H

The letter H is drawn with two tall bars and a crossbar. Describe the lines.

1. The two tall bars are parallel.
2. The crossbar meets each bar at a right angle, so it is perpendicular to both.

Answer: two parallel bars with a crossbar perpendicular to each.

Tip: parallel does not mean the lines have to be horizontal. Two slanted lines can also be parallel.

Why it matters

Parallel and perpendicular lines are the basis of buildings, roads, maps and grids. Builders check that walls are perpendicular to floors, and the next lessons use these ideas to name angles and shapes.