Can you make sense of these three proofs of Pythagoras' Theorem?
P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?
Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.
Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?
Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.
Engage in a little mathematical detective work to see if you can spot the fakes.