01 / QUICK RECAP
Connect the ideas.
- Identify a right angle and the opposite hypotenuse first.
- The equation compares square areas, not a sum of side lengths.
- Add leg squares for a hypotenuse; subtract from its square for a leg.
- Use consistent units and take a positive root for a length.
- Keep exact roots or round only at the final step.
- Use the converse carefully, and distinguish a final height from a change in height.
02 / TOPIC TEST
Put it together.
Choose a paper and show your working.
Pythagoras’ theorem — topic test
A progressive topic paper with calculations, explanations and practical applications.
15 questions · 37 marks · 45 minutes · By hand
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics (2026)
Hypotenuse and right-angled triangles; why the theorem works; finding the hypotenuse; finding a shorter side; exact roots versus rounded answers; checking whether a triangle is right-angled; practical length problems.
Official curriculum source ↗