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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-Y9-06NZC26-P4-MEA-MEA-P-Y9-07NZC26-P4-MEA-MEA-P-Y10-10NZC26-P4-MEA-MEA-K-Y9-08
Resources
- CorbettMaths on using Pythagoras’ theory to find sidesQuestions PDF · Answers
- Beta: Various from chapter 21
Terminology
- Pythagoras' theorem
- hypotenuse
- short side
- long side
- right angle
- right-angled triangle
- square root
Task goals
- Identify the hypotenuse as the longest side, opposite the right angle, before writing $a^2+b^2=c^2$.
- Find a missing hypotenuse by adding the squares of the two shorter sides, then taking the square root.
- Find a missing shorter side by subtracting a known square from the hypotenuse's square, then taking the square root.
- Leave an answer as a simplified surd such as $\sqrt{19}$ when it is not a perfect square, unless asked to round.
Where this fits
What leads into this objective, and where it goes next.
Before
Measurement applications: SOHCAHTOA
Perimeter and area of composite shapes involving circles
Circumference and area of circles
You are here
Pythagoras theory finding short and long sides
Do
Using Pythagoras' theorem to: verify that given side lengths in a right-angled triangle satisfy the theorem; find the length of the hypotenuse in a right-angled triangle, given the lengths of the other two sides
Statement▸
Year 9 · Measurement · Measuring
NZC26-P4-MEA-MEA-P-Y9-06
Do
Proving Pythagoras' theorem (e.g. by rearranging four congruent right-angled triangles into a square)
Statement▸
Year 9 · Measurement · Measuring
NZC26-P4-MEA-MEA-P-Y9-07
Also under GM5-10:
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.