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 ;
Both statements provided are true according to fundamental geometric principles. The first statement is always true due to the parallel postulate, and the second statement is also always true because perpendicular lines to the same line are indeed parallel. The answers are A for both questions.
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