1. For which of these finite geometries of Chapter 1 does Euclid's fifth postulate always hold:
Solution: Actually, as angle measurement is not a part of these finite geometries, Euclid's fifth postulate in its original form does not apply to them. However, using the equivalent Playfair's axiom, we can make sense of this question. Only the Geometry of Pappus, of the ones listed above, satisfies this axiom.
2. For the thirteen-point finite geometry of this section, name all the lines through point A that do not have a point in common with BDF.
Solution: AGJ; AIL; AKM
For exercises 7-15 refer to the figure below. Assume the parallels to AB through C are CD and CE.
For exercises 7-12 tell whether the pair of lines are intersecting, parallel or nonintersecting.
7. CI and CE are intersecting.
8. CF and AG are nonintersecting.
9. CG and AB are intersecting.
10. CE and DF are intersecting.
11. CJ and GB are intersecting.
12. CD and IG are intersecting.
13. How do you know that angle ICG is congruent to angle GCE?
Solution: They are angles of parallelism for the same segment.
14. Would it be possible for angle GCF to be a right angle? Why?
Solution: Yes. The angle GCE is acute, and angle GCF is greater.
15. Would it be possible for angle GCJ to be an obtuse angle? Why?
Solution: No. Angle GCE is acute and angle GCJ is smaller.