Why do this problem?

It provides experience of generalising a result from 2 dimensions to an equivalent result in 3 dimensions. This problem asks the question for them but learners should be encouraged to ask themselves "What if..." and always to think about possible generalisations.

Key questions

What comes to mind when a problem involves squares of distances?
If we are looking for Pythagoras theorem where are the right angles triangles?

Possible extension

The problem Pythagoras for a Tetrahedron.