Pythagoras harder problems

A set of challenging activities using Pythagoras’ theorem.

Activities included:

Starter:
Given two isosceles triangles, pupils work out which one has the larger area.

Main:
Examples/practice questions, followed by two sets of questions on the theme of comparing area and perimeter of triangles. Both sets start with relatively straight forward use of Pythagoras’ theorem, but end with an area=perimeter question, where pupils ideally use algebra to arrive at an exact, surd answer.

Plenary:
Not really a plenary, but a very beautiful puzzle (my take on the spiral of Theodorus) with an elegant answer.