The problems in this feature offer students the chance to investigate geometrical properties, make conjectures and create convincing mathematical proofs.
Many of the problems in this feature include proof sorting activities which challenge students to rearrange statements in order to recreate clear, rigorous proofs. These tasks aim to introduce students to the formality and logic of mathematical proof.
You can watch a recording of the webinar in which we discussed the mathematical thinking which can be prompted by these activities.
Plus magazine has a selection of interesting articles exploring proofs in which pictures play an important role.
Circumference angles
Can you prove the angle properties described by some of the circle theorems?
Cyclic Quadrilaterals Proof
Can you prove that the opposite angles of cyclic quadrilaterals add to $180^\circ$?
Pythagoras Proofs
Can you make sense of these three proofs of Pythagoras' Theorem?
Pentakite
Quad in Quad
Matter of Scale
Overlap
A red square and a blue square overlap. Is the area of the overlap always the same?
Kite in a Square
The Converse of Pythagoras
Can you prove that triangles are right-angled when $a^2+b^2=c^2$?
To swim or to run?
We are very grateful to the Heilbronn Institute for Mathematical Research for their generous support for the development of these resources.