Lines

CBC Grade 5 Mathematics — Lines

Lesson Objectives

By the end of this topic, a learner should be able to:

• Identify and draw horizontal and vertical lines
• Identify and draw perpendicular lines
• Identify and draw parallel lines
• Appreciate the use of these line types in everyday situations

Lines

A line is straight and goes on in both directions. This topic names lines by the way they lie and by how they meet.

a) Horizontal lines

A horizontal line goes flat, from side to side.

The word comes from horizon, the flat line where the land meets the sky.

The top of a table is horizontal. So is a shelf, and the surface of still water in a cup.

b) Vertical lines

A vertical line goes straight up and down.

A standing pole is vertical. So is the edge of a door. So is a rope with a weight hanging from it.

A builder hangs a string with a stone tied to it. The string always hangs vertically, so it shows whether a wall is upright.

c) Telling them apart

Horizontal goes across. Vertical goes up.

Here is a way to remember. The horizon is flat. Something vertical points at the sky.

d) Perpendicular lines

Two lines are perpendicular when they cross at a right angle.

A right angle is a square corner. The corner of this page is one.

A horizontal line and a vertical line are perpendicular to each other.

We mark a right angle with a small square drawn in the corner.

e) Drawing perpendicular lines

Use a set square. The corner of a piece of card works too.

Draw the first line. Place the square corner against it. Draw the second line along the other edge.

Check with the corner of a book afterwards. It should fit exactly.

f) Parallel lines

Two lines are parallel when they stay the same distance apart and never meet.

Railway lines are parallel. So are the lines on ruled paper, and the two long edges of a door.

However far you draw them, they never touch.

g) Drawing parallel lines

Use a ruler and a set square.

Draw the first line along the edge of the set square. Keep the set square pressed against the ruler and slide it along. Then draw the second line.

Sliding keeps the same angle, and that is what makes the lines parallel.

Measure the gap in two places to check. It should be the same.

h) Where this is used

A builder checks walls and floors. A carpenter marks square corners. A farmer plants in parallel rows. A road painter marks lanes.

:::checkpoint Check yourself

1. Which way does a horizontal line go?
2. Give one example of a vertical line.
3. What angle do perpendicular lines make?
4. Why do parallel lines never meet? :::

Definitions

• Horizontal line — a line running flat, side to side.
• Vertical line — a line running straight up and down.
• Perpendicular lines — two lines meeting at exactly 90°.
• Parallel lines — two lines that never meet, same distance apart throughout.

Must Remember

1. Perpendicular lines meet at exactly 90°.
2. Parallel lines never meet, however far extended.
3. These are relationships between two lines, not properties of one line alone.
4. Horizontal/vertical describe one line's direction; perpendicular/parallel describe how two lines relate.

Conclusion

This topic names specific relationships between lines - some about a single line's direction, some about how two lines relate to each other.