Pythagoras' theorem

Can you make sense of these three proofs of Pythagoras' Theorem?

Can you minimise the amount of wood needed to build the roof of my garden shed?

Can you make sense of the three methods to work out what fraction of the total area is shaded?

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

What is the perimeter of this unusually shaped polygon...

How does the perimeter change when we fold this isosceles triangle in half?

What does Pythagoras' Theorem tell you about the radius of these circles?

Can you calculate the length of this diagonal line?

What is the same and what is different about these circle questions? What connections can you make?

Weekly Problem 2 - 2009
The 16 by 9 rectangle is cut as shown. Rearrange the pieces to form a square. What is the perimeter of the square?