Through a point not on a line, one and only one line can be drawn parallel to the given line. always sometimes never 10. two coplanar lines that are perpendicular to the same line are parallel. always sometimes never

The parallel postulate: In a plane there can be drawn through any point A, lying outside of a straight line a, one and only one straight line which does not intersect the line a. This straight line is called the parallel to a through the given point A.

Therefore, first statement is always true.

Coplanar lines are lines that lie on the same plane.

Theorem: If two coplanar lines are perpendicular to the same  line, then the two lines are parallel to each other.

Therefore, second statement is always true.

1st question: always

2nd question: always

Step-by-step explanation:

1st question

Given a line and a point which is not on that line, there is only one new line parallel to the old line which pass through the point. That is, there are infinity new lines parallel to the old line, but only one of them pass through the given point.

2nd question

If two coplanar lines are parallel and intercept a third line, then the same angle is formed in the interception between each parallel line and the third line. In this case a 90° angle is formed and each parallel line is perpendicular with the third line.

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.

noncoplanar points are points that do not lie on the same line.