We then develop some Euclidean geometry using cross ratios. Some samples:
For three points
,
and
with
distinct from
and
,
.
Two triangles
and
are similar iff
.
Four points are concyclic or collinear iff their cross ratio is real.
, 
and 
with distinct from and , 
.
and 
are similar iff 
.
, and with distinct from and , .
and are similar iff .