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Can you arrange line in a plane so they're perpendicular but don't intersect?
NO. Perpendicular lines in the same plane alwaysinthersect.
What are lines that lie in the same plane and intersect at right angles?
Perpendicular lines.
Two lines in the same plane that intersect at a right angle are?
perpendicular lines.
How are parallel lines perpendicular to the same line?
If you have two parallel lines, then they have the same slope. If you have another line, in the same plane as the first two lines, and it is not parallel to them, then the angle of intersection with the first line will be the same as the angle of intersection with the second line. If this angle is 90°, then the third line is perpendicular to the first line and also to the second line. For an example, think of a rectangle. Two opposite sides are parallel. Now pick one of the 3rd or 4th sides. Each of these sides is perpendicular to both the first side and the second side.
In a plane if two lines are perpendicular to the same line then are they parallel to each other?
So long as all three lines are in the same plane, yes.
