lengths are 'relative' in Euclidean geometry


In a book I'm reading it says that 'In Euclidean geometry lengths can
be measured only in terms of some arbitrary unit BECAUSE SIMILAR
NONCONGRUENT FIGURES EXIST.'

Can someone explain how the capitalized part is a determining factor
for whether length units are arbitrary or not for a geometry? I
understand why length is arbitrary in Euclidean geometry, but my
understanding has nothing to do with "figures," but rather that length
can not be defined with respect to anything in the Euclidean plane
(i.e., like how right angles can be 'defined' as the angle produced by
erecting a line on a given line in such a way that the two angles
produced are equal).

.

Relevant Pages

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