Question

2. Theorem 2-10 states that through a point not on a line, there

Answer 1

When two or more lines are parallel to each other, this implies that they do not meet even extending them till infinity. So the statement justifies the construction because only one line through point C can be constructed to be parallel to AB.

When a parallel line is constructed through a point to a given line, this is the only parallel line that can be drawn to the given line. Parallel lines are lines that will not meet at any point. Thus, only one parallel line can be constructed through a point not to a given line.

The construction of a line through C that is parallel to line AB is justified by the given statement in the theorem since this is the only parallel line to line AB that can be drawn through the point C. Any other line through C would intersect or meet line AB at a point when extended, thus would not be parallel to the given line.

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