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.