Two coplanar lines that are parallel or perpendicular are either parallel or perpendicular.
True
False
Could be true and false
I answered "Could be true and false"
Actually, the correct answer is "True".
When two lines are coplanar (meaning they lie in the same plane), if they are parallel or perpendicular, then they will always be either parallel or perpendicular to each other. This is a fundamental property of parallel and perpendicular lines.
To understand why this is true, we can consider the conditions for two lines to be either parallel or perpendicular.
Two lines are parallel if they never intersect, and they have the same slope. When two parallel lines are coplanar, any other line that intersects one line will also intersect the other line at the same angle. Therefore, all intersections between the two lines and the other line will be parallel.
Two lines are perpendicular if they intersect at a right angle (90 degrees). When two perpendicular lines are coplanar, any other line that intersects one line will also intersect the other line at a right angle. Therefore, all intersections between the two lines and the other line will be perpendicular.
Thus, if two lines are coplanar and they are either parallel or perpendicular, they will always be either parallel or perpendicular to each other. Hence, the statement "Two coplanar lines that are parallel or perpendicular are either parallel or perpendicular" is true.