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11+ Maths Guide · Year 5–6 · Free lesson

Parallel and Perpendicular Lines

Railway tracks and page edges: parallel. Walls and floors: perpendicular. This lesson pins down both definitions, their diagram marks, and the often-forgotten third option — neither.

G14Parallel and Perpendicular Lines
Never meeting vs meeting at 90°.
Parallel lines never meet; perpendicular lines cross at a right angle.
Two special line relationships.
Parallel — same direction, never meet
marked with matching arrows
Perpendicular — cross at exactly 90°
marked with a small square
Railway tracks: parallel. A wall and the floor: perpendicular.
1

Learn the Definitions

1Parallel lines.

Always the same distance apart — they never meet, however far you extend them. Marked with matching arrowheads.

⇉ never meet

2Perpendicular lines.

Cross (or meet) at exactly 90°. Marked with the little square.

⊥ at 90°

3Spot them in shapes.

A rectangle: 2 pairs of parallel sides, and every neighbouring pair perpendicular.

▭
💡 Key IdeaLines can be neither — crossing at 60° is neither parallel nor perpendicular. The two words are specific, not opposites.
2

Worked Example

Parallel, perpendicular or neither?

Opposite sides of a square
parallel
Neighbouring sides of a square
perpendicular
Two sides of an equilateral triangle
neither (60°)
3

Watch Out! Common Mistakes

✕
‘Parallel-ish’.

All or nothing! Lines are only parallel if they NEVER meet — nearly-parallel lines eventually cross, so they aren’t parallel.

✕
Perpendicular must look upright.

Wrong! Perpendicular is about the 90° angle, not the orientation — a tilted + is still perpendicular.

✕
Everything is one or the other.

No! Lines crossing at 60° are neither parallel nor perpendicular. Check the angle before naming.

⬇ Cheat Sheet

PARALLEL AND PERPENDICULAR LINES
  1. Parallel: same direction, never meet (arrow marks).
  2. Perpendicular: meet/cross at exactly 90° (square mark).
  3. Crossing at any other angle: neither.
  4. Rectangle: opposite sides parallel, adjacent sides perpendicular.
Example: square → opposite sides parallel, neighbours perpendicular.

📖 Continue Your Journey

✓ G1 2D Shapes✓ G2 Triangles✓ G3 Quadrilaterals✓ G4 Regular and Irregular Polygons✓ G5 Circles✓ G6 3D Shapes✓ G7 Nets✓ G8 Types of Angles✓ G9 Measuring and Drawing Angles✓ G10 Angles on a Line and at a Point✓ G11 Angles in Triangles✓ G12 Angles in Quadrilaterals✓ G13 Vertically Opposite AnglesG14 Parallel and Perpendicular LinesG15 SymmetryG16 Coordinates (First Quadrant)G17 Coordinates (Four Quadrants)G18 TranslationG19 ReflectionG20 Geometry Problem Solving
→
Next Lesson: G15 SymmetryFold it — do the halves match?
📄 Free printable: Download the Parallel and Perpendicular Lines cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Frequently asked questions

What are parallel lines?

Lines that run in the same direction, always the same distance apart, and never meet however far they're extended — like railway tracks. Diagrams mark them with matching arrowheads.

What does perpendicular mean?

Meeting or crossing at exactly 90°, shown by a small square at the join — like the corner of a page.

Can lines be neither parallel nor perpendicular?

Yes — any lines crossing at an angle other than 90°, like two sides of an equilateral triangle (60°).

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