| The final isometry of the disc is when the two
reflecting lines are ultra parallels.
In the three previous cases a vertex and its image where all equidistant
from a particular object:
-
the reflecting line for the reflection isometry
-
the point of intersection for the elliptic isometry
-
the centre point of the horocycle circle for the parabolic isometry
In this case it is the unique d-line that is perpendicular to the
two ultra parallels. Now a vertex and its image lie on the hypercycle shown
and hence are equidistant from this perpendicular d-line.. |
|
Congruent triangles
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