(1) can be proved directly. Divide the quadriliateral into two quadrilaterals by joining the midpoints of the base and the summit. Now use the result that the greater summit angle in a quadrilateral always lies opposite the greater arm.
this is of course all in hyperbolic geometry...
I have a couple of questions that are puzzling me. These first two are what i really need help. thank you for any help!
1. how do you prove that the summit of a saccheri quadrilateral is longer than the base? i know you prove by contradiction, and I know how to prove that the summit is not equal to the base, so really, how do you prove that the summit is not shorter than the base?
2.prove that there are pairs of parallel lines that do not admit a common perpendicular. this i am just stuck on. must this have something to do again with that angle of parallelism, ultra parallel, etc?
(1) can be proved directly. Divide the quadriliateral into two quadrilaterals by joining the midpoints of the base and the summit. Now use the result that the greater summit angle in a quadrilateral always lies opposite the greater arm.