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## 'Thebault's Theorem' printed from http://nrich.maths.org/

It gives an opportunity for experimentation and making your own
conjecture, which then needs to be proved. Three different methods
of proof are based on coordinates, vectors and complex
numbers.

### Key questions

Four points are vertices of a parallelogram. What do you know about
the line segments joining them?

If on a line segment you draw a square:

- what do you know about the vertices of the square?
- can you find the coordinates, or the position vector of the
centre of the square?

### Possible support