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.