Could someone give a proof of "The line through a given point and parallel to a given line can be drawn".
I would be able to do this myself but I am so confused on the wording. As in what are we given initially? A point and a line or just a point?
2026-03-28 20:50:40.1774731040
Line through a given point
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You're given a line and a point, and you wish to draw a line through that given point parallel to the line that you were given.
This is known as Playfair's Axiom and is equivalent to the parallel postulate (also known as Euclid's fifth postulate). We can prove that these two are equivalent, but you cannot prove one by itself (many attempts in the past to prove just the parallel postulate have been made however).