How two lines can relate
Two straight lines on a flat surface can do one of two things: they meet, or they never meet.
| Relationship | What happens | Symbol | Example |
|---|---|---|---|
| Parallel lines | Never meet; always the same distance apart | ∥ | railway tracks |
| Intersecting lines | Cross at one point | the letter X | |
| Perpendicular lines | Cross at a right angle (90°) | ⊥ | the corner of a page |
Perpendicular lines are a special kind of intersecting lines.
Parallel lines
Parallel lines run side by side like train tracks. However far you extend them, they never touch. On diagrams, matching arrowheads on the lines show they are parallel.
Examples: the lines on lined paper, opposite edges of a ruler, the top and bottom of a door.
Intersecting lines
Intersecting lines cross at one point of intersection. When they cross, they make four angles. Angles opposite each other are equal (called vertically opposite angles).
Perpendicular lines
Perpendicular lines meet at exactly 90°, forming four right angles. A small square drawn in the corner shows a right angle.
Examples: the corner of a window, the plus sign +, the x-axis and y-axis on a graph.
Checking for perpendicular
Use the corner of a piece of paper or a set square. If the corner fits exactly into the angle, the lines are perpendicular.
Transversals
A transversal is a line that crosses two or more other lines. When a transversal crosses parallel lines, it creates pairs of equal angles. You’ll study these in later grades.
Shapes and line relationships
| Shape | Parallel sides | Perpendicular sides |
|---|---|---|
| Square | 2 pairs | 4 right angles |
| Rectangle | 2 pairs | 4 right angles |
| Parallelogram | 2 pairs | usually none |
| Trapezoid | at least 1 pair | sometimes |
| Right triangle | none | 1 pair |
Worked examples
Example 1: The letter H: what kind of lines are the two upright strokes?
Parallel.
Example 2: The letter T: what kind of lines?
Perpendicular: they meet at a right angle.
Example 3: Two roads cross at a sharp angle like a narrow X. Are they perpendicular?
No, they are intersecting but not at 90°.
Common mistakes
- Thinking all intersecting lines are perpendicular. Only 90° crossings are.
- Thinking lines must be horizontal to be parallel. Slanted lines can be parallel too.
- Judging by short segments. Two segments might not touch but still not be parallel; extend them to check.
Try it yourself
- What symbol means "is parallel to"?
- Name the angle formed by perpendicular lines.
- Are the lines in the letter E parallel, perpendicular, or both?
- Name an object with parallel edges.
Answers: 1) ∥ 2) a right angle (90°) 3) both 4) e.g. a book, a door, a ruler
Quick recap
- Parallel lines never meet.
- Intersecting lines cross at a point of intersection.
- Perpendicular lines meet at a right angle.