Checking whether a triangle is right-angled

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.