Primary 3 · Measurement & Geometry
P3 perpendicular and parallel lines
Parallel lines never meet, however far you extend them. Perpendicular lines meet at a right angle, a square corner. In P3, your child spots both in a figure, names them with letters, and draws them on a square grid.
- Taught in
- Term 3
- Syllabus
- 2 skills
- Usual slip
- Trusting the drawing
What your child learns in P3 perpendicular and parallel lines
Two skills, each with what it looks like on a worksheet.
See the syllabus wording
- perpendicular and parallel lines
- drawing perpendicular and parallel lines
Spot them and name them
Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. Both can be slanted, not only flat or upright. Schools write AB // CD for parallel and EF ⊥ GH for perpendicular.
Draw them on a square grid
Count the squares a line moves: 3 across and 1 up. A parallel line repeats that count. A perpendicular line swaps the numbers and turns the other way: 1 across, 3 down. Off a grid, use a set square.
Key facts and formulas
- Perpendicular linesTwo lines that meet at a right angle are perpendicular.
- Parallel linesParallel lines stay the same distance apart. They never meet.
- Lines in a rectangleAB is parallel to DC. AB is perpendicular to BC.
- Drawing themHold a ruler still. Slide a set square along it for a parallel line. Use its square corner for a perpendicular line.
Words to know
- Parallel lines
- Lines that stay the same distance apart and never meet, however far they go.
- Perpendicular lines
- Lines that meet at a right angle.
- Right angle
- A square corner, like the corner of a book.
- Extend
- Carry a line on past where it is drawn, to see whether it meets another.
- Set square
- The triangle ruler with a square corner, used to draw a right angle.
The sentence that costs the mark
These two lines do not cross on the page. Are they parallel?
What the working usually does
as drawnthe lines=parallel
On the page the two lines do not touch, so they look parallel. The drawing is doing the deciding.
What the question asked
extendedthe lines=not parallel
Carried on, the gap narrows and the two lines meet. So they are not parallel.
Two lines that lean slightly towards each other can stop before they touch, so "not touching" passes for "parallel". On a grid, check the slant: for the same squares across, does each line go up the same number of squares? If not, they meet somewhere.
The same P3 perpendicular and parallel lines question, worked properly
Lah works through it the way she does every question in StudyLah: one step at a time, marking the picture as she goes.
Identify the pair of parallel lines in the figure below.
- Parallel lines never meet, even when we extend them. On a grid, they have the same slant.
- BC and EF never touch, and both lean the same way. But BC goes 1 down for every 1 across, and EF goes 2 down for every 1 across.
- So BC and EF would meet if we extend them. AB and DE both go straight across, so they never meet.
- So the parallel pair is AB and DE.
Every question in StudyLah comes with a walkthrough like this one.
Try it freeThree quick P3 perpendicular and parallel lines questions
Try them together, then tap to check.
Question 1
Look at the square grid below. Name the line that is parallel to JK.
Show answer
AnswerLM. From J to K is 3 squares across and 4 down. From M to L is also 3 across and 4 down, so the slants match.
Question 2
Which line is perpendicular to line AB?
Show answer
AnswerEF. AB goes 4 squares across and 2 up. EF goes 2 across and 4 down, the two numbers swapped, so extended they meet at a right angle.
Question 3
The figure shows the front of a kitchen cabinet. Which pair of lines is parallel: AC and JK, EG and CD, JK and CD, or FH and AB?
Show answer
AnswerJK and CD. Both run straight across the cabinet and stay the same distance apart. Each of the other pairs meets at a square corner.
Helping at home
How to tell it has clicked
Draw two lines that lean slightly towards each other but stop before they touch. Ask if they are parallel. A child who says no, because they would meet further on, has it. One who says yes because they do not cross is reading the picture.
Turn the page so a parallel pair is slanted. If your child still finds it, they are using the rule, not looking for lines that run straight across.
Try this tonight
Railway tracks and the two long edges of a table stay the same distance apart, so they are parallel. The two edges of a pizza slice do not touch on the plate, but follow them and they meet at the tip.
Hunt for square corners: where a wall meets the floor, or the corner of a book. Check one with the corner of a sheet of paper. Those lines are perpendicular.
Before and after P3 perpendicular and parallel lines
Builds on
Primary 3 AnglesCompares angles with a square corner
You are here
Primary 3 Perpendicular and Parallel Lines
Spots and draws parallel and perpendicular lines
Leads to
Primary 4 Rectangles and SquaresKnows which sides and corners must match
Leads to
Primary 5 Parallelogram, Rhombus and TrapeziumFinds angles from parallel and equal sides
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StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.