A free printable parallel lines and transversals worksheet for Grade 8 math.
By Kris Reddy, Ontario teacher · Updated October 17, 2026 · 22 questions (30 marks) · PDF + answer key
This free parallel lines and transversals worksheet teaches Grade 8 students the angle relationships formed when a transversal crosses two parallel lines. Students name six types of angle pairs on a numbered diagram, find unknown angles and give a reason for each one, and solve for x using corresponding, alternate and co-interior angles.
The second page asks students to decide whether lines are parallel from their angles, find two unknowns in one diagram, solve three real-world problems about railway tracks, a carpenter's brace and shelves, and correct two common mistakes. Every diagram is drawn to scale from its true angles, and every answer was checked by computer. To print it, use the Download button above.
| Part | Skill practised | Marks |
|---|---|---|
| A | Name 6 angle pairs on a numbered diagram | 6 |
| B | Find 4 angles and give reasons | 4 |
| C | Solve for x (3 diagrams) | 6 |
| D | Are the lines parallel? (3 diagrams) | 3 |
| E | Find x and y in one diagram | 3 |
| F | Three real-world problems | 6 |
| G | Spot the mistake | 2 |
The parallel lines and transversals worksheet supports the Ontario Grade 8 math curriculum in the Spatial Sense strand, where students use the angle properties of intersecting and parallel lines to solve problems. Part C also practises solving equations, so it pairs well with the two-step equations worksheet.
A transversal is a line that crosses two other lines. Each crossing makes four angles, so there are eight in total. The arrows (>) on the blue lines show that they are parallel: they never meet, no matter how far they go.
Angles 3, 4, 5 and 6 sit between the parallel lines, so they're called interior angles. Angles 1, 2, 7 and 8 are exterior. Part A of the parallel lines and transversals worksheet uses this exact numbering.
Every pair of angles in the diagram either is equal or adds to 180°. The shapes (F, Z, C) help students spot each pair quickly.
| Angle pair | Shape | Where | Example | Rule |
|---|---|---|---|---|
| Corresponding | F | Same position at each crossing | ∠1 and ∠5 | Equal |
| Alternate interior | Z | Between the lines, opposite sides | ∠3 and ∠6 | Equal |
| Alternate exterior | — | Outside the lines, opposite sides | ∠2 and ∠7 | Equal |
| Vertically opposite | X | Across from each other at one crossing | ∠5 and ∠8 | Equal |
| Co-interior | C | Between the lines, same side | ∠4 and ∠6 | Add to 180° |
| Linear pair | — | Side by side on a straight line | ∠1 and ∠2 | Add to 180° |
A useful shortcut: in this kind of diagram every angle is either the small (acute) one or the big (obtuse) one, and the two sizes always add to 180°. So once you know one angle, you know all eight. That's the idea behind Part B. For the formal geometry, see transversal (geometry) on Wikipedia.
When angles are written as expressions, decide first whether the pair is equal or supplementary, then write an equation.
For co-interior angles, add the expressions and set the total to 180° instead. Always substitute x back in to check that both angles make sense.
The rules also work backwards. If corresponding or alternate angles are equal, or co-interior angles add to 180°, the lines must be parallel. If the angles don't follow the rules, the lines aren't parallel. Part D of the parallel lines and transversals worksheet includes one pair of lines that is only 6° off parallel, which is hard to see but obvious from the angles.
These questions match the parallel lines and transversals worksheet PDF, which has every diagram drawn to scale.
Open each part to check the parallel lines and transversals worksheet answers. The printable key is on the last two pages of the PDF.
These are the errors that come up most when marking this parallel lines and transversals worksheet. Part G targets two of them directly.
For more practice, try the geometry shapes and properties quiz and the algebra basics quiz.
Yes. The worksheet and its answer key are free to download and print as one PDF, with no account needed.
A transversal is a line that crosses two or more other lines. Where it crosses two lines it makes 8 angles, numbered 1 to 8 on this worksheet.
Corresponding angles, alternate interior angles, alternate exterior angles and vertically opposite angles are equal. Co-interior angles and angles on a straight line add to 180°.
Check a pair of angles made by a transversal. If corresponding or alternate angles are equal, or co-interior angles add to 180°, the lines are parallel. If not, they aren't.
It is written for Grade 8 math and also works as Grade 9 geometry review.
Ready to start? Use the Download button above to print the free parallel lines and transversals worksheet double-sided, and keep the answer key pages for marking.