Question 160104: prove two statements below are equivalent.
If two line cut by transversal, the interior angles on one side of the transversal add to less than 180, then two lines will meet on that side of the transversal.
given a line and point not on the line, there exist a unique line through the point that is parallel to the given line.
I can prove them separately but I do not know how o make a connection between the two.
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! i think the answer lies in the fact that when the sum of the interior angles is less than 180, the lines will meet on that side of the transversal.
i believe this also implies that when the sum of the interior angles is greater than 180, the lines will also meet, only on the other side of the transversal.
this implies that the only time when the lines can be parallel is when the sum of the interior angles is exactly 180.
since there can only be one line where the sum of the interior angles is 180, that line is unique.
you should be able to prove that when the sum of the interior angles is 180, the lines are parallel as follows:
top interior angle on left is x.
bottom interior angle on left is (180-x)
bottom interior angle on right is x (supplementary)
alternate interior angles are =.
lines are parallel.
-----
|
|
|
