In response to SuperSaiyanGokuX
I am positive that they were lines, because it did have the line drawn above it. Anyways, thanks for all of you that clarified. I guess its just that if theoretically, if you took line PS and line SR, saying they WERE two lines, and placed them on their points, they would overlap at S and infinitely number of points.
In response to XxDohxX
If there's just a line drawn above the letters that indicate the endpoints, then it's just a line segment. If there's a line with arrows on each end, then it's a line.
In response to XxDohxX
XxDohxX wrote:
Well, to clarify, it was talking about the whole line itself, and naming the line--line PS and line SR.
I forgot to include that.

Anyways, but the definition said it needed TWO lines. I don't see how one line can be two.

Explain to me how ONE line ends up being TWO. :-(

Okay, simple equation time. If you're dealing with full lines--which you're not in this case--then you can have two identical lines.

Two equations:
y=x
2y+3=2x+3

Both are considered separate lines because they came from different equations, but they're really identical. If you compute an intersection for them, you find that they intersect on an infinite number of points. They are only one line in the sense that they operate in the same space, but if you simply phrase the problem to say that one is line A and the other is line B, then you can intersect them. This doesn't screw with the postulate because the postulate is concerned with lines that are not identical. Obviously in every geometry system (Euclidean geometry is just one kind), identical lines will have an infinite number of common points. You are incorrect to say they are merely one line, because the problem outright told you there are two; that the lines are identical does not change that.

In the case of the problem at hand, the wording of the problem clearly indicates that PS and SR are line segments, not full infinite lines. Therefore an intersection would be any parts of them that touch. That could be a single point if they cross or if they share a common endpoint, or another line segment if they occupy the same line. For instance, the intersection of US and UT is US. Since PS and SR share only one point in common, S, that is the intersection.

Your teacher was right; you misinterpreted the problem. 1) You're not dealing with lines, just line segments. 2) The postulate in question only applies to two different lines, or to line segments on two different lines. 3) If the problem says there are two lines, then there are two; if they overlap you still can't ignore that there are two of them.

Lummox JR
In response to Lummox JR
Thats why its a postulate and not a theorem because it is just accepted as correct and not proven. I hate postulates, their evil >.<
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