MATH 6118-090
Non-Euclidean Geometry
Exercise Set #6
1.
If is a triangle
and
is the
associated Saccheri quadrilateral, show that
is a Saccheri
quadrilateral with base DE and summit
AB.
2.
Prove
the following in the hyperbolic plane: If is a triangle
and
is the
associated Saccheri quadrilateral, then
.
3.
Prove
the following in Euclidean geometry: If T
is the triangular region corresponding to the right triangle with right
angle at C, then
.
4.
This
is an exercise in Euclidean geometry. For each of the following pairs of
rectangles, find explicit triangulations of each such that corresponding
triangles are congruent.
a.
The square and the
rectangle.
b.
The square and the
rectangle.
c. The square and the
rectangle.