Primary 3 · Mathematics

P3 perpendicular and parallel lines

Two lines that do not cross on the page are not always parallel. Most marks here are lost calling lines parallel because they do not touch, when, extended, they would meet. Here is the test that settles it.

Level: P3
Usually taught: Term 3
Covers: 1 concept

What changes at P3

In Primary 3, your child learns to spot two relationships between straight lines: parallel, lines that run in the same direction and never meet, and perpendicular, lines that cross at a right angle. It is naming what lines do, the start of geometry.

The one thing to get right is what "parallel" really means: never meeting, however far the lines are extended, and always the same distance apart. Two lines that just happen not to cross on the page are not automatically parallel.

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

Extended, the gap narrows and the two lines would meet, so they are not parallel.

Two slightly-angled lines really do not cross in a short drawing, so "not touching here" looks like "parallel". Parallel means never meeting even if the lines run on forever, always the same distance apart. Extend them, or check the gap at both ends, before deciding.

Parallel: the gap is the same at both ends, so the lines never meet.

Not parallel: the gap narrows, and the dashed extensions show the lines would meet.

The same question, worked properly

Do not decide from the drawing alone
not crossing here ≠ parallel
On a short drawing, two lines that lean towards each other can still fail to touch. "They do not cross" is not the test. The test is whether they would EVER meet.
Extend the lines and watch the gap
gap narrows → they would meet → not parallel
This is the step that fails. Follow both lines further than they are drawn. If the gap gets smaller, they are heading for a meeting point, so they are not parallel. Deciding from the drawn part alone is exactly where the mark is lost.
Parallel stays equal; perpendicular meets at 90°
parallel: same gap all along
Parallel lines keep the same distance apart forever, so the gap is equal at both ends. Perpendicular is the other property here: two lines that meet at a right angle, a square corner. Test that one with the corner of a set square.

How can you tell it has clicked?

Draw two lines that lean slightly towards each other but do not touch, and ask if they are parallel. A child who extends them, sees them meet, and says no has understood it. One who says yes because they do not cross is reading the drawing, not the rule.

The check for parallel is the gap: measure it at both ends. The same gap means parallel; a changing gap means they would meet. For perpendicular, the check is the right angle where the lines cross.

One thing to try tonight

Railway tracks and the two long edges of a table stay the same distance apart however far they run, which is parallel. The two straight edges of a pizza slice look like they do not meet on the plate, but follow them and they reach the point. Extend before deciding.

Hunt for right angles around the house, where a wall meets the floor, or the corner of a book, and call those lines perpendicular. Then find lines that never get closer, the shelves of a bookcase, and call those parallel.

What your child will meet in this topic

Parallel and Perpendicular

Most Singapore schools introduce this in Term 3, though schools do differ by a term either way. If your child’s school runs a different order, you can set it in the schedule on your dashboard.

What it leads to

Parallel and perpendicular run through the rest of geometry: the sides of squares, rectangles and other shapes in P4 and P5 are described by which are parallel and which meet at right angles. Getting the two properties clear now makes those shapes easy to reason about.

The "extend and see" habit is also the groundwork for angles and coordinate geometry later, where lines are followed well beyond the part you can see. A child who checks rather than eyeballs keeps that edge.

More in Primary 3

Other topics in the same year, so you can see what sits either side of this one.

Struggling with the working rather than the topic itself? How to help your child with problem sums

See how your child is doing on this topic

StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.

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