# Proof reading

- Cambridge Mathematics
- Mathematical Salad
- Proof reading

## Proof reading

I have been thinking about proof for many, many years now (at least a decade. Maybe two. Maybe three…).

So instead of writing, meandering around some idea, here’s a visual selection of some of my favourite geometrical proofs ever… the question is, can you identify the theorem or what they prove?

**The area of the large square is double the area of the small square; the square’s side lengths are the smallest possible co-prime pair.**

You can tweet us the solutions @CambridgeMaths or comment below, and feel free to send us some of your own geometrical proofs!

**Some ideas for the classroom: **

**Early years and lower primary**

Using link cubes show that

- an even number plus an even number is always even
- an odd number plus an odd number is always even
- an even plus an odd number is always odd

**Upper primary**

Use this diagram and your knowledge of angles to explain why vertically opposite angles are equal.

**Early secondary**

Find two different ways to express the area of this trapezium to prove Pythagoras’ theorem.

**Upper secondary**

Use the diagram below to help explain why the gradients of perpendicular lines are negative reciprocals of one other.