Congruence for angles has the usual Euclidean meaning. If two u-lines
intersect at a point A, the number of degrees in the angle they
make is by definition the number of degrees in the angle between
their tangent rays at A (see Figure 24).
 Figure 24
Given:
Three points A, B and C in the upper
half-plane.
The angle determined by u-lines AB
and AC under the upper half-plane model.
Constructions:
 Figure 25
-
Let the perpendicular bisector
of A and B intersect the x-axis at P. Construct the line
b through A and perpendicular to  .
-
Let B' be the intersection of b and the line,
which is parallel to
 and passes
through B.
-
The construction of C' with
respect to A and C is similar to that of B' with respect to
A and B.
-
The hyperbolic angle determined
by B, A, C with vertex A is then the Euclidean angle determined
by B', A, C' with vertex A.
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