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Can a line have a midpoint or bisector?
If you mean a line segment, then yes, every line segment has a midpoint. However, some ideas of a line define it as going on forever in a certain plane, so if is it a line without beginning or end, then it can't really have a midpoint since there is nothing to measure from. You would have to define a starting and ending point before it could have a midpoint.
Can two planes intersect in a ray or a segment explain why?
In 3d space, two planes will always intersect at a line...unless of course they are the same plane (they coincide). Because planes are infinite in both directions, there is no end point (as in a ray or segment). So, your answer is neither, planes intersect at a line.
Given two points A and B in the three dimensional space what is the set of points equidistant from A and B?
A plane is the set of all points in 3-D space equidistant from two points, A and B. If it will help to see it, the set of all points in a plane that are equidistant from points A and B in the plane will be a line. Extend that thinking off the plane and you'll have another plane perpendicular to the original plane, the one with A and B in it. And the question specified that A and B were in 3-D space. Another way to look at is to look at a line segment between A and B. Find the midpoint of that line segment, and then draw a plane perpendicular to the line segment, specifying that that plane also includes the midpoint of the line segment AB. Same thing. The set of all points that make up that plane will be equidistant from A and B. At the risk of running it into the ground, given a line segment AB, if the line segment is bisected by a plane perpendicular to the line segment, it (the plane) will contain the set of all points equidistant from A and B.
What parallel lines intersect?
Parallel lines in the Euclidean plane do not intersect but all parallel lines in the projective plane intersect at the point at infinity.
Two lines that on the same plane that never intersect?
parallel lines If they are not on the same plane and never intersect they are skew
