Exercises 1-4 refer to the Klein model.

1. Draw a triangle with three ordinary points as vertices

2. Draw an omega triangle.

3. Draw a triangle with exactly two ideal vertices.

4. Draw a triangle with three ideal vertices.

Solutions 1-4:

Exercises 6-10 refer to the Poincaré model.

6.Draw an example of an angle of parallelism.

7. Draw an omega triangle.

8. Draw a triangle with exactly two ideal vertices.

9. Draw a triangle with three ideal vertices.

10. Draw a Saccheri quadrilateral.

Solutions 5-9:Note that the numbering of the answers is off by 1.

11. In Figure 9.43, find the distance AD, using the formula given.

Solution:In the formula, replace C by A to get AD = k ln (AA/AB)/(AD/DB). Since AA is zero and none of the other quantities are zero, we have AD = k ln(0) = -infinity, i.e., this line has infinite length.