Triangle investigation [ GM4.3 Extension Starter] Write down two whole numbers, and then: find the sum of the squares of the two numbers (answer 1) find the difference between the squares of the two numbers (answer 2) double the product of the two numbers. (answer 3) If the three answers 1, 2 and 3 above are the lengths of sides of a triangle what is special about the triangle? Investigate. Preamble A short investigation for individual pupils involving the recognition of Pythagorean triplets (but not by this name). Possible content Using squares of numbers and recognising Pythagoras’ theorem and that it applies to a right-angled triangle. Resources None. Solution/Notes The numbers generated are the sides of right-angled triangles i.e. (answer 1)² = (answer 2)² + (answer 3)². Original Material © Cambridge University Press 2010 Original Material © Cambridge University Press 2010