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Geometrical Reasoning
Creating convincing arguments or "proofs" to show that statements are always true is a key mathematical skill. The problems in this feature offer you the chance to explore geometrical properties, make conjectures and create proofs to show that these are always true.
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.
Circumference Angles
Age 11 to 16
Challenge Level 
Can you prove the angle properties described by some of the circle theorems?
Cyclic Quadrilaterals Proof
Age 11 to 16
Challenge Level
Can you prove that the opposite angles of cyclic quadrilaterals add to $180^\circ$?
Pythagoras Proofs
Age 11 to 16
Challenge Level
Can you make sense of these three proofs of Pythagoras' Theorem?
Matter of Scale
Age 14 to 16
Challenge Level
Can you prove Pythagoras' Theorem using enlargements and scale factors?
Overlap
Age 14 to 16
Challenge Level
A red square and a blue square overlap. Is the area of the overlap always the same?
Pentakite
Age 14 to 18
Challenge Level
Given a regular pentagon, can you find the distance between two non-adjacent vertices?
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?
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?
The Converse of Pythagoras
Age 14 to 18
Challenge Level
Can you prove that triangles are right-angled when $a^2+b^2=c^2$?
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Patterns in Number Sequences
These resources are designed to get you thinking about number sequences and patterns.