Sample Exam Questions for Final

1.Determine whether the following statements are true or false:

1. _____ If two triangles are equivalent, they have the same defect.

2. _____ In hyperbolic geometry, some, but not all, convex quadrilaterals have an angle sum of 360^o.

3. _____ The line joining the midpoints of the equal sides of a Saccheri quadrilateral is perpendicular to both sides.

4. _____ If two triangles are similar in the Poincaré model, then they are congruent.

5. _____ In hyperbolic geometry, every line segment has a unique perpendicular bisector.

2. The centuries long search for a proof of Euclid's parallel postulate was doomed to failure. Write a short paragraph explaining why.

3. In any Saccheri quadrilateral, show that the segment joining the midpoints of the base and summit, and the segment joining the midpoints of the two equal sides are perpendicular.

4. a) In the Poincaré model, draw an example of a Lambert quadrilateral one of whose vertices is at the center of the model.
b) In hyperbolic geometry, it is possible to have a line parallel to both of two intersecting lines. In the Poincaré model, draw an example of this phenomenon.