Prove that the following statement is equivalent to euclid's 5^th postulate,  
If a straight line intersects one of two parallel lines, it will always intersect the other.

Suppose that the lines l and k are parallel and line m intersects k at a point. We will use the playfair form of the Euclidean fifth postulate.
If m does not intersect l, then m is parallel to l. This would mean that there are two parallels to l through P(m and k). contradicting play fair's axiom. Thus, m must also intersect l. Now let P be a point and l a line not through P. we can construct a line parallel to l through P, call it k. Let m be any other line through P. Since it intersects one of two parallel lines (k), it must intersect the other (l) by assumption. thus, there is only one line through P which is parallel to l.