Lines
3.0 Geometry · 3.1 Lines
Syllabus tag: Kenya CBC | Grade 6 Mathematics | Strand 3.0 Geometry | Sub-Strand 3.1 Lines (6 Lessons)
Lesson objectives
By the end of this topic, you will be able to:
- Draw parallel lines
- Bisect lines by construction
- Construct perpendicular lines
- Appreciate the use of lines in daily life
Lines
A line is straight and has no thickness. This topic draws lines in special positions using a ruler and a pair of compasses.
a) Parallel lines
Parallel lines run side by side and never meet, however far you draw them.
The distance between them is the same all the way along. That is what makes them parallel.
Railway lines are parallel. So are the lines on ruled paper, and the opposite sides of a door.
We mark parallel lines with small arrowheads pointing the same way.
b) Drawing parallel lines
Use a ruler and a set square.
Place the set square against the ruler and draw the first line along its edge. Then slide the set square along the ruler and draw the second.
Sliding keeps the same angle, and that is why the lines stay parallel.
c) Bisecting a line
To bisect means to cut into two equal halves.
Open the compasses to more than half the line.
Put the point at one end and draw an arc above and below the line. Move to the other end and, without changing the opening, draw two more arcs.
Join the two crossing points. That line cuts the first one exactly in half.
Keeping the same compass opening is what makes it work. Changing it gives a line that is not through the middle.
d) Perpendicular lines
Perpendicular lines cross at a right angle, which is 90°.
The bisector you just drew is perpendicular to the first line. So one construction gives you both.
We mark a right angle with a small square in the corner.
The corner of a room is perpendicular. So is the corner of this page, and the cross on a window frame.
e) Constructing a perpendicular at a point
Choose a point on the line. Put the compass point there and draw an arc cutting the line on both sides.
Then bisect the piece between those two cuts.
The bisector passes through your chosen point at a right angle.
f) Where this is used
A builder checks a wall corner. A carpenter marks a straight cut. A tailor lays out cloth. A footballer marks a pitch with square corners.
Words to know
- Parallel lines — two lines that never meet and stay the same distance apart along their whole length.
- Perpendicular lines — two lines that meet at a right angle (90°).
- Bisect — to divide something into two exactly equal parts.
- Midpoint — the exact middle point of a line, equally distant from both ends.
:::checkpoint Check yourself
- What is special about parallel lines?
- What does bisect mean?
- Why must the compass opening stay the same when bisecting a line?
- What angle do perpendicular lines make? :::
Bridge to practice
Try the exercises below — identifying and reasoning about parallel lines, bisected lines, and perpendicular lines in real-life and constructed examples.