Mathematics 7–10 · Year 7
A transversal on parallel lines: measuring the three angle relationships
Measurement and space
The idea
When a transversal crosses parallel lines, corresponding angles are equal, alternate angles are equal and co-interior angles add to 180 degrees, and none of these hold when the lines are not parallel.
What you need
- Lined A4 paper (the printed lines are parallel)
- Ruler, set square and protractor
- A second sheet with two lines drawn deliberately non-parallel (about 10 degrees apart)
How to do it
- On lined paper draw a transversal crossing two of the printed lines at any angle other than 90 degrees; label the eight angles a to h.
- Measure all eight angles with the protractor and record them.
- Identify the corresponding pairs, the alternate pairs and the co-interior pairs; check equal pairs differ by at most 2 degrees and co-interior pairs sum to 180 within 2 degrees.
- Repeat on the non-parallel sheet and record which relationships fail and by how much.
- Use a set square slid along a ruler to draw your own parallel pair and confirm the relationships hold again.
What you should see
On the lined paper the eight angles take only two sizes, which sum to 180 (for a transversal at 50 degrees to the lines: four angles of 50 and four of 130); corresponding and alternate pairs agree within the ±1 degree reading error and co-interior pairs sum to 178 to 182. On the non-parallel sheet with lines 10 degrees apart, corresponding angles differ by about 10 degrees and co-interior pairs sum to about 170 or 190, so the relationships fail by the same 10 degrees the lines are out of parallel. The learner knows it worked when the failure on the second sheet matches the angle between the lines.
What changes
- What you change
- whether the two lines are parallel
- What you measure
- difference between corresponding angles
- What you keep the same
- same transversal angle
- same protractor
- angles read at the vertex
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Alternate angles are equal for any pair of lines.
- Co-interior angles are equal rather than supplementary.
- Vertically opposite angles need the lines to be parallel.
Safety card
Hazards
No hazard is listed.
Controls
No control is listed.
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; ordinary classroom supervision.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Mathematics K–10 Syllabus (2022), Stage 4 Angle relationships; page read 2026-09-22MA4-ANG-C-01
- Australian Curriculum v9AC9M7M04
Sources
The pages the author read to write this activity.