Pythagoras — NSW Year 8 Maths
Right-angled triangles, from ladders against walls to the diagonal of a TV screen. Seven subtopics and 140 practice questions, each with a fully worked solution, aligned to NESA outcome MA4-PYT-C-01.
Pythagoras in NSW Year 8
Pythagoras' theorem links the three sides of a right-angled triangle: the square on the hypotenuse, the longest side, equals the sum of the squares on the two shorter sides, \(c^2 = a^2 + b^2\). It is new in Year 8, and it lets students find a missing length without measuring and check whether a triangle really has a right angle.
The seven subtopics below start with calculations involving square roots, then find the hypotenuse, find a shorter side, test for right-angled triangles and Pythagorean triads, and finish with mixed problems and word problems. Pythagoras is one of the 14 topics in NSW Year 8 Maths and sits in the Measurement and Space strand (NESA outcome MA4‑PYT‑C‑01, with the square-root work drawing on MA4‑IND‑C‑01). In Stage 5 it leads on to trigonometry and to the distance between two points on the number plane.
Subtopics
Pythagoras: common questions
What is Pythagoras' theorem in Year 8 maths?
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the two shorter sides: \(c^2 = a^2 + b^2\). For shorter sides of 6 cm and 8 cm, \(c^2 = 36 + 64 = 100\), so the hypotenuse is 10 cm.
How do you find a shorter side using Pythagoras' theorem?
Subtract instead of adding: square the hypotenuse, take away the square of the known shorter side, then take the square root. If the hypotenuse is 13 m and one side is 5 m, \(b^2 = 169 - 25 = 144\), so the other side is 12 m.
How can you tell if a triangle is right-angled?
Square the longest side and compare it with the sum of the squares of the other two sides. If they are exactly equal, the triangle is right-angled. For sides 7, 24 and 25, \(49 + 576 = 625 = 25^2\), so it is.
Which NESA outcome covers Pythagoras' theorem?
Pythagoras' theorem sits in Stage 4 of the NSW Mathematics K–10 Syllabus (2022) under outcome MA4‑PYT‑C‑01, usually taught in Year 8. The square-root skills in the first subtopic come from the indices outcome MA4‑IND‑C‑01.
What comes after Pythagoras in Year 8?
Pythagoras' theorem is used again for areas and perimeters of shapes with sloping sides and for distances on a grid. In Stage 5 it supports trigonometry, where right-angled triangles are used to find unknown angles as well as sides.