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What are all of the point on a plane that are the same distance from a single point called the center?

That's called a "circle".


What is called when two lines are not in the same plane and do not intersect?

I believe this is possibly called a vector. They begin at the same point, however, they do not run on the same plane, nor do the intersect. As I said, they do begin at the same point and form a triangle.


What is if two lines lies in the same plane and have more then one point in common?

They must be the same identical line, otherwise it's impossible.


Point A lies outside of plane P. How many planes can be drawn parallel to plane P that pass through point A?

There is exactly one plane that can be drawn parallel to plane P that passes through point A. Since parallel planes share the same orientation and direction, any plane that is parallel to plane P must maintain the same angle and distance from the points on plane P. Therefore, the plane through point A will be uniquely defined and parallel to plane P.


Point A lies outside of plane P how many lines can be drawn parallel to plane P that pass through point A?

Only one line can be drawn parallel to plane P that passes through point A. This line will be oriented in the same direction as the plane, remaining equidistant from it. All other lines passing through point A will either intersect the plane or be skew to it.


What is the set of points in a plane that are same from a givin point called the center?

This is the definition of a circle


How do you determine if a point lies on the same line?

A point lies on a line if the coordinates of the point satisfy the equation of the line.


The set of all points in a plane that are the same distance from a given point?

circle, but the given end point is called the center of a circle : )


What term applies to two lines in the same plane if they have no common plane?

If they are in the same plane, then they share a common plane. Did you mean to say common point. If that's the case where they are in the same plane, but do not share a common point, then they are parallel lines.


What is a point that do not lie on the same plane?

a truthfull point


Point that lies on the same line?

ray


What are points in the same plane called?

Points that are within the same plane are called co-planer.