Category:Isometries (Euclidean Geometry)

This category contains results about Isometries (Euclidean Geometry).
Definitions specific to this category can be found in Definitions/Isometries (Euclidean Geometry).

Let $\EE$ be a real Euclidean space.

Let $\phi: \EE \to \EE$ be a bijection such that:

$\forall P, Q \in \EE: PQ = P'Q'$

where:

$P$ and $Q$ are arbitrary points in $\EE$

$P'$ and $Q'$ are the images of $P$ and $Q$ respectively

$PQ$ and $P'Q'$ denote the lengths of the straight line segments $PQ$ and $P'Q'$ respectively.

Then $\phi$ is an isometry.