Rephrase the first paragraph of Section 8.3 in your own words, and justify
everything.
Prove that HPP (the Hyperbolic Parallel Postulate) <=> There exist
parallel lines l and m with a transversal line t such that the alternate
interior angles formed by l, m, and t are not congruent. (Hint: For the
"=>" direction, use Proposition 8.3.1. For the
"<=" direction, use Problem I above. Prove the
"<=" direction first, as it's easier.)
(This problem has nothing to do with hyperbolic geometry; it just gives us
more practice with Section 2.4; so assume the EPP.)
Show that in a quadrilateral ÿABCD,
mÐA
+ mÐC
= 180o and
mÐB
+ mÐD
= 180o iff ÿABCD
can be inscribed in a circle.
[Optional: True of false? In a quadrilateral ÿABCD,
if mÐA
+ mÐC
= 180o, then ÿABCD
can be inscribed in a circle.]