Testing for Right Angled Triangles

Three side lengths are enough to tell whether a triangle has a right angle. In NSW Year 8 maths this test, the converse of Pythagoras' theorem, compares the square of the longest side with the sum of the squares of the other two (NESA outcome MA4‑PYT‑C‑01).

You will choose the longest side as \(c\), work out \(a^2 + b^2\) and \(c^2\), and answer yes only when the two are exactly equal. You will name the angle that is \(90^\circ\), test sides given in mixed units, as decimals or with a surd like \(\sqrt{5}\), and choose a third side that makes a right angle. Builders check that the corner of a garden bed is square in the same way. It is part of Year 8 Pythagoras.