Stage: 4 Challenge Level: 
Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line?
Dynamical systems. Long problems. Squares. Mathematical reasoning & proof. Number theory. Visualising. Generalising. Pythagoras' theorem. Manipulating algebraic expressions/formulae. Inequality/inequalities.
Published June 2000.
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