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.
Answer:
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.
