Thread: Euclids Fifth Postulate and High School Postulate

In order to solve both of these problems below I need to understand the proof. I know that both of these problems are interchangeable but I do not believe my work is correct.

1) On a plane EFP and HSP are equivalent. If we assume EFP is true then I can show that if l is a line and p is a point not on l, than there is a line through p that does not intersect l and then this line will be unique.

I have that line l and l' are two parallel straight lines. Line m intersects both l and l'. According to Euclids Fifth Postuale a and c are same side interior angles. This is as far as I have got with solving this proof. Any help would be wonderful!

2) If we assume that HSP is true, than I can show how l and l' are cut by a transversal m, and if the sum of the measures of the interior angles is less than 180 degrees l and l' must intersect on that side of the transversal l.

I know that this question is just like the question stated above. But without the proof above I also cannot solve this question. Any help in solving these problems would be amazing.

EFP states: If a striaght loine intersecting two straight lines makes the interior angles on the same side less than two right angles, then the two lines (if extended indefinitely) will meet on that side on which are the angles less than two right angles.


HSP states: For every line l and ever point P not onl line l, there is a unique line l' that passes through P and does not intersect (is parallel to) l.



Any help on answering the EFP and HSP Postulates? Please??



For part 1 we need to show that EFP and HSP are equivalent on the plane, you need to show that you can prove EFP if you assume HSP and vise versa. If the three postulates are eqwuivalent, than you can prove the equiavlence.