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Do Through a point not on a line one and only one line always can be drawn parallel to the given line?
True
Only one plane can pass through one line and a point that is not on the line?
I'd feel a lot more comfortable if you said "... can contain one line and a point ...".When you say "pass through one line", I picture a sword passing through a tight pieceof string. If that's how your plane passes through the line, then the statement in your"question" is false. If your plane contains the line and the extra point, then the statementis true ... only one plane can do that.
What is Euclid's parallel postulate?
Although he presented it differently, the modern version is as follows:given a straight line and a point which is not on that line, there is only one line which will pass through the point and which is parallel to the line.
How do you graph a line with one point?
If you're only given one point, you can't draw the graph of the line, because there are an infinite number of different lines that all go through that one point. Or, to put it another way, if someone gives you a single point and asks you to draw the line through it, you can draw any old line you want through that point, and nobody can say it's wrong. In order to pin it down to one unique line, you need another piece of information in addition to the one point: either the slope of the line, or another point.
What postulate or theorem guarantees that there is only one line that can be constructed perpendicular to a given line from a given point not on the line?
It's the theorem that says " One and only one perpendicular can be drawn from a point to a line. "
