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Many of the problems in this feature include proof sorting activities which challenge you to rearrange statements in order to recreate clear, rigorous proofs.
Plus magazine has a selection of interesting articles exploring proofs in which pictures play an important role.
problem
Pentakite
Age
14 to 18
Challenge level
Given a regular pentagon, can you find the distance between two non-adjacent vertices?
problem
Kite in a square
Age
14 to 18
Challenge level
Can you make sense of the three methods to work out what fraction of the total area is shaded?
problem
The converse of Pythagoras
Age
14 to 18
Challenge level
Can you prove that triangles are right-angled when $a^2+b^2=c^2$?
problem
Quad in quad
Age
14 to 18
Challenge level
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
problem
To swim or to run?
Age
16 to 18
Challenge level
The famous film star Birkhoff Maclane wants to reach her refreshing drink. Should she run around the pool or swim across?
We are very grateful to the Heilbronn Institute for Mathematical Research for their generous support for the development of these resources.