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## 'Pythagoras Proofs' printed from http://nrich.maths.org/

### Why do this problem?

This
problem shows three different approaches to Pythagoras'
Theorem. It could be used with a group who have recently met the
theorem to provide a variety of ways of thinking about it, or with
a group who are familiar with the theorem, to explore different
methods of proof. There are great opportunities for communicating
mathematical ideas and debating which method appeals the most and
why!

### Possible approach

Divide the class into small groups and assign each group one
of the proofs to work on. Explain that once they understand how the
proof works they will be asked to produce a poster or presentation
to persuade others of the value of their proof.

After allowing plenty of time for exploring their proof and
producing their explanation, bring groups together so that each
group can present their proof to others who have worked on a
different proof. Everyone should get the opportunity to see all
three proofs explained. Encourage learners to be (constructively)
critical of each other's proofs and to question points that aren't
clear.

Finally, bring the whole class back together for a vote on
which proof they thought was the clearest and most satisfying, and
a discussion on the merits of each proof.

### Key questions

What exactly are you trying to prove?

What do you know? What can you work out
from what you know?

Does each step you have written down follow on
directly from the last one?

Are all the assumptions you have made valid
ones?

### Possible extension

Read more about proof

here.
### Possible support

Tilted
squares can be used to introduce ways of
proving Pythagoras' Theorem.