Pythagoras' theorem.
Explain Pythagoras’ theorem, choose the correct side equation and solve right-triangle problems with appropriate exactness.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Hypotenuse and right-angled triangles
Identify the hypotenuse from the right angle before choosing a formula.
- 02
Why the theorem works
Explain the theorem using areas rather than treating it as a rule to memorise.
- 03
Finding the hypotenuse
Add squared leg lengths and take the positive root to find a hypotenuse.
- 04
Finding a shorter side
Subtract a known leg square from the hypotenuse square to find the other leg.
- 05
Exact roots versus rounded answers
Choose exact roots or rounded lengths and state the requested accuracy.
- 06
Checking whether a triangle is right-angled
Use the converse to decide whether three given side lengths form a right triangle.
- 07
Practical length problems
Turn a practical diagram into a right-triangle calculation and interpret the length found.
Topic review
Revisit the key ideas, then choose a practice paper.