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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.
How do you find all the places equidistant from to lines?
If the two lines are coplanar, then it is a third, parallel, line which is halfway between the two lines. If the two lines are not in the same plane, then I think it will be a saddle shape (paraboloid).
Are two lines parallel to a third line parallel to each other?
Yes.
What are the three relationships for two straight lines in the same plane?
Well, there are really only two: parallel and intersecting. Parallel lines go in the same direction and never cross; intersecting lines do cross (or intersect). However, a third relationship, that's actually a special case of intersecting lines, is the case of perpendicular lines. Perpendicular lines are those that make four right angles when they intersect. Really, it's enough if you know that only one of the angles is a right angle - the rest follow automatically.
Are perpendicular lines perpendicular to a third line?
Yes. Take a look at the corner of your room, where two walls meet the floor.
