Angles, Polygons and Geometrical Proof

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

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

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.

Why does this fold create an angle of sixty degrees?

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

Is it possible to find the angles in this rather special isosceles triangle?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?