Geometrical reasoning can involve coordinate geometry and properties of 2d and 3d shapes, and may even lead to algebraic representations. These problems invite you to explore geometry in a variety of contexts.
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
Can you describe this route to infinity? Where will the arrows take you next?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Can you make sense of the three methods to work out the area of the kite in the square?
This article gives a brief history of the development of Geometry.