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## Main Question or Discussion Point

It's been a long time since I've studied geometry, and had an extremely poor instructor at the time, so I'm having difficulty remembering how to prove certain theorems. My linear algebra is a bit rusty as well, though I'm more well versed in that than in geometry. One of my students needs help and I'm at a loss as to how to explain this. The theorem in question is that:

Any Euclidean transformation can be obtained as a composition of Euclidean reflections in hyperplanes.

I'm aware that a proof by induction is required of the base case in R^1, and then an inductive proof of the theorem in R^n. Beyond that, if someone could remind me of what needs to be to prove such a thing, it'd be much appreciated.

Any Euclidean transformation can be obtained as a composition of Euclidean reflections in hyperplanes.

I'm aware that a proof by induction is required of the base case in R^1, and then an inductive proof of the theorem in R^n. Beyond that, if someone could remind me of what needs to be to prove such a thing, it'd be much appreciated.