Mathematics 7–10 · Year 9
Compass constructions: bisectors and an equilateral triangle, then measured
Measurement and space
The idea
Constructions made with a compass and straight edge produce equal lengths and equal angles by design, and measuring the result with a ruler and protractor confirms the properties the construction guarantees.
What you need
- Compass with a locking radius, sharp pencil, ruler, protractor
- Plain A4 paper
How to do it
- Draw an interval AB of 10.0 cm. With the compass set wider than 5 cm, draw arcs from A and from B above and below the interval; join the two crossing points. Measure the two parts of AB and the angle at the crossing.
- Draw an angle of about 70 degrees. From the vertex draw one arc cutting both arms; from the two cuts draw equal arcs that cross; join the vertex to the crossing. Measure the two halves.
- Draw an interval of 8.0 cm; with the compass set to 8.0 cm draw arcs from each end that cross above; join to make the triangle. Measure all three sides and angles.
- Write each construction as a numbered algorithm of compass and ruler steps that another learner can follow without seeing the drawing, then swap and test.
- Explain each result with congruent triangles (for the bisector, the four points form a rhombus).
What you should see
The perpendicular bisector cuts AB into two parts of 5.0 cm each (within 1 mm) and meets it at 90 degrees (within 1 degree). The angle bisector gives two halves of about 35 degrees each, equal within 1 degree. The equilateral triangle has three sides of 8.0 cm and three angles of 60 degrees within reading error. The learner knows it worked when a partner following only the written algorithm produces a figure with the same measured properties.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- A construction needs the ruler's markings to be accurate.
- The perpendicular bisector is any line through the midpoint.
- Equal arcs guarantee equal lengths only if the compass is measured against a ruler.
Safety card
Hazards
- compass point
Controls
- carry the compass closed
- keep the point on the paper
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 5 Properties of geometrical figures B (Path); covers the congruence tests that explain each construction in step 5, because neither the Stage 4 nor the Stage 5 geometry content includes ruler-and-compass construction; page read 2026-09-22MA5-GEO-P-01
- Australian Curriculum v9AC9M9SP03
Sources
The pages the author read to write this activity.