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Learning objective overview
Master Teaching Guide coverage for this objective.
Current NZC (2007)
GM5-10
New NZC (2026)
NZC26-P4-MEA-MEA-P-Y10-10
Resources
- CorbettMaths — Showing a triangle is right-angled (video)
- CorbettMaths on Pythagoras' theoremQuestions PDF · Answers
Terminology
- Pythagoras' theorem
- converse of Pythagoras
- right-angled triangle
- hypotenuse
- Pythagorean triple
Task goals
- Apply the converse of Pythagoras' theorem to test whether $a^2+b^2=c^2$ holds for given side lengths.
- Identify the longest side first, then compare the sum of squares of the two shorter sides against the square of the longest.
- Distinguish between right-angled and non-right-angled triangles by checking the exact equality, not an approximation.
- Recognise scaled Pythagorean triples (e.g. 6, 8, 10 as a scaled 3, 4, 5) and explain why they remain right-angled.
Where this fits
What leads into this objective, and where it goes next.
You are here
Checking whether a triangle is right-angled
Do
Using Pythagoras' theorem to: find the length of an unknown side in a right-angled triangle; check if a triangle has a right angle; calculate the distance between two points in the coordinate plane, yielding the distance formula d = √((x2 − x1)^2 + (y2 − y1)^2)
Statement▸
Year 10 · Measurement · Measuring
NZC26-P4-MEA-MEA-P-Y10-10
Also under GM5-10:
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.