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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
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?