Primary 3 Perpendicular and Parallel Lines Study Guide

Primary 3 perpendicular and parallel lines in four short steps: spotting each kind of line pair, then drawing each one through a point with a ruler and a set square. Each step has something to try, and worked examples follow.

Start here

What are perpendicular and parallel lines?

Perpendicular lines meet at a right angle. Parallel lines stay the same distance apart, so they never meet.

A set square has a corner that is a right angle. It checks the first kind of line pair, and with a ruler it draws both kinds. Your child uses these two tools all through this chapter.

In this chapter your child learns to:

  • spot perpendicular lines with the corner of a set square;
  • spot parallel lines by counting the gap at both ends on a square grid;
  • draw a line through a point, perpendicular to a given line;
  • draw a line through a point, parallel to a given line, and mark both lines.
1

Step 1

Identifying perpendicular lines

Lines that meet at a right angle are perpendicular lines. Put the corner of a set square where the two lines cross, with one edge along the first line. If the second line lies exactly along the other edge, the lines are perpendicular, even when both of them slope. We mark the right angle with a small square. Crossing lines are perpendicular only when they meet at a right angle.

Decide, then let the set square check

A
B
C
D
Is each pair perpendicular? Choose, then the set square checks your answer.
Try it

Two roads on a map cross each other. Are they perpendicular?

▶ Watch the lesson: Name line pairsPractise 19 questions →
2

Step 2

Identifying parallel lines

Lines that stay the same distance apart never meet. On a square grid, count straight up from one line to the other at each end. If the gap is the same at both ends, the lines are parallel, and we mark them with matching arrowheads. Parallel lines can slope. If the gap changes, the lines get closer at one end, and made longer they would meet.

Raise or lower M

12312345MGLH
Count straight up from G to L: 3 squares. From H to M: 1 square. The gap changes, so LM is not parallel to GH. The lines get closer towards M; made longer, they would meet.
Try it

Line CD is 3 squares above GH at the left end. How many squares above GH must it be at the right end for CD to be parallel to GH?

▶ Watch the lesson: Name line pairsPractise 19 questions →
3

Step 3

Drawing perpendicular lines with a set square

A perpendicular line meets the given line at a right angle. The corner of a set square is a right angle, so its two edges are perpendicular. Place a ruler along the line, put the set square against the ruler, and slide it until its edge touches the point. The new line must pass through the point. Draw it, move the tools aside, and mark the right angle.

Press Next step

Draw a line through P that is perpendicular to GH. The new line must pass through P.
Try it

The ruler is along GH and the set square is against the ruler. What do you do next?

▶ Watch the lesson: Draw a perpendicularPractise 7 questions →
4

Step 4

Drawing parallel lines with a set square

A parallel line keeps the same direction as the given line, so the two never meet. Put one edge of the set square along the line, then put a ruler along another edge. The ruler keeps the set square from turning, so as it slides along the ruler, its edge keeps the same direction. Stop when the edge reaches the point, draw the line, and draw matching arrows on both lines.

Press Next step

Draw a line through P that is parallel to GH. The new line must pass through P.
Try it

When you draw a parallel line, why do you hold the ruler still against the set square?

▶ Watch the lesson: Draw a parallelPractise 7 questions →

Primary 3 perpendicular and parallel lines questions, worked step by stepTry each one with a pencil, a ruler and a set square first. Then open the hint, or reveal each working step in turn.

Name line pairsBasic

The diagram shows three lines on a square grid. Which line is perpendicular to AB? Which line is parallel to AB?

Use the corner of a set square for one question. Count squares at both ends for the other.
  1. Put the corner of a set square where AB and CD cross, with one edge along AB.
  2. CD lies exactly along the other edge, so CD meets AB at a right angle.
  3. Count straight up from A to E: 3 squares. From B to F: 3 squares.
  4. The gap stays the same, so EF and AB never meet.
Answer: CD is perpendicular to AB. EF is parallel to AB.
Name line pairsBasic

Lines PQ and RS are drawn on a square grid. Is RS parallel to PQ? Write Yes or No.

Count straight up from PQ to RS at the left end, then at the right end.
  1. Count straight up from P to R: 3 squares.
  2. Count straight up from Q to S: 4 squares.
  3. The gap changes from 3 squares to 4 squares, so the lines do not stay the same distance apart.
Answer: No
Name line pairsIntermediate

Figure ABCD is drawn on a square grid. (a) Name a pair of parallel lines. (b) Name two pairs of perpendicular lines.

Check each corner with a set square. Then count squares between the two lines that run across.
  1. Count straight up from AB to D: 3 squares. From B to C: 3 squares. The gap stays the same, so AB is parallel to DC.
  2. At B, the corner of a set square fits exactly, so AB is perpendicular to BC.
  3. At C, the corner fits again, so BC is perpendicular to DC.
  4. AD slopes. It does not meet AB or DC at a right angle.
Answer: (a) AB is parallel to DC. (b) AB is perpendicular to BC, and BC is perpendicular to DC.
Draw a perpendicularIntermediate

Use a ruler and a set square to draw a line through X perpendicular to YZ. Mark the right angle.

The ruler goes along YZ, not through X.
  1. Place a ruler along YZ.
  2. Put the set square against the ruler.
  3. Slide it until its edge touches X.
  4. Draw along that edge through X, down to YZ.
  5. Lift the set square and the ruler aside, then mark the right angle.
Answer: A straight line through X that meets YZ at a right angle, with a small square marking the right angle.
Draw a parallel and a perpendicularChallenge

(a) Draw a line through K parallel to LM. (b) Draw a line through K perpendicular to LM. (c) Which of your new lines do you mark with matching arrows, and which line gets a right-angle mark?

Use the set-square moves for each line, then think about what each mark shows.
  1. (a) Put the set square along LM and a ruler along the set square. Slide the set square to K and draw the line.
  2. (b) Place the ruler along LM, put the set square against it, and slide until its edge touches K. Draw the line.
  3. The line in (a) keeps the same direction as LM, so it and LM get matching arrows.
  4. The line in (b) meets LM at a right angle, so a small square marks the right angle where it meets LM.
Answer: (c) The line in (a) gets matching arrows, with LM. The line in (b) gets a right-angle mark where it meets LM.
5

Step 5

Check yourself

Five quick questions on line pairs and set-square drawing. Nothing is saved. Each answer points to the perpendicular or parallel practice to try next.

1. Perpendicular lines meet at…

2. Two lines cross, but the corner of a set square does not fit where they meet. Are they perpendicular?

3. On a square grid, CD is 2 squares below GH at both ends. What are CD and GH?

4. You are drawing a line through point P, perpendicular to GH. Where must the new line go?

5. You have drawn a line through P parallel to GH. What do you mark?

0/5
Answer all five to see where to practise next.
For parents

How to use this guide. Each step takes a few minutes. Before your child presses a button, ask them to say what they expect. Will the set square fit? Will the gap stay the same? Which edge will they draw along? Saying it first, then checking, is how the picture sticks.

Real tools help most in this chapter. A ruler and a set square on plain paper are what the drawing questions ask for, so let your child copy Steps 3 and 4 by hand. Look for line pairs at home together: the edges of a door, window bars, the lines on a road. Then try the worked examples, revealing one line of working at a time.

More study guides

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Lessons and practice

P3 Perpendicular and Parallel Lines lessons and practice

3 lesson videos and 45 questions across three subtopics, from Basic to Challenge, each with a worked solution.

Watch and practise →