Pythagoras Theorem — NSW Year 9 Core Maths
Squares, roots and surds, then Pythagoras' theorem: finding sides, testing for right angles, triads and worded problems. Eight subtopics and 160 practice questions with worked solutions, aligned to MA4-PYT-C-01 and MA5-IND-P-02.
Pythagoras Theorem in NSW Year 9
Pythagoras' theorem connects the three sides of a right-angled triangle: \(c^2 = a^2 + b^2\), where \(c\) is the hypotenuse, the longest side. In Year 9 Core the theorem is revised from Stage 4 and taken a step further, with exact answers left as surds, triangles described by their vertices instead of a diagram, and problems that need more than one step.
The eight subtopics below start with squares, square roots and surds, then state the theorem, find the hypotenuse and a shorter side, mix the two, test whether a triangle is right-angled, explore Pythagorean triads and finish with worded problems. Pythagoras Theorem is one of the 13 topics in NSW Year 9 Core Maths and sits in the Measurement and Space strand. It revises NESA outcome MA4‑PYT‑C‑01, and the surd work comes from MA5‑IND‑P‑02. Right-angled triangles lead straight into Year 9 trigonometry and into finding the length of an interval on the number plane.
Subtopics
Pythagoras Theorem: common questions
What is Pythagoras' theorem?
In a right-angled triangle, the square of the longest side (the hypotenuse) is equal to the squares of the two shorter sides added together: \(c^2 = a^2 + b^2\). The hypotenuse always faces the right angle.
How do you find the hypotenuse?
Square the two shorter sides, add them and take the square root. For sides of \(9\) cm and \(12\) cm, \(c^2 = 81 + 144 = 225\), so \(c = 15\) cm.
How do you find a shorter side?
Subtract instead of adding. Square the hypotenuse, take away the square of the known shorter side, then take the square root. For a hypotenuse of \(25\) and a side of \(7\), \(x^2 = 625 - 49 = 576\), so \(x = 24\).
How can you tell if a triangle is right-angled?
Add the squares of the two shorter sides and compare the total with the square of the longest side. For \(5\), \(12\) and \(13\), \(25 + 144 = 169 = 13^2\), so the triangle is right-angled. If the two numbers differ, it is not.
Which NESA outcome covers Pythagoras' theorem in Year 9?
Pythagoras' theorem is Stage 4 content under MA4‑PYT‑C‑01, revised in Year 9 Core. The surd work in this topic, such as writing an answer as \(5\sqrt{10}\), comes from the Stage 5 outcome MA5‑IND‑P‑02.