Line and Plane Relationships

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When we studies the relative position between two geometrical figures, we want to find the possible relationships that can occur. In the next table guide are presented, first the relationships existing between two lines and, after that, the existing relationship between a line and a plane.

Parallel linesTwo Parallel linesParallel lines are always the same distance apart from each other — no matter how far they are extended, they will never meet.
Perpendicular LinesTwo Perpendicular LinesTwo lines are perpendicular or orthogonal if they meet at right angles.
Coincident lines Two Coincident lines Coincident lines are lines that lie exactly on top of each other. These lines have all points in common.
Parallel Line and PlaneParallel Line and PlaneWhenever there is no meeting point between a line and a plane, then we can say that the line is parallel to the plane.
Perpendicular Line and PlanePerpendicular Line and PlaneIf a line and a plane have only one point in common, then the line intersects the plane. If the line forms a right angle with any of the lines contained in the plane then the line is perpendicular to the plane.
Oblique Line and PlaneOblique Line and PlaneAs in the previous example, this line also intersects the plane, but since it does not form a right angle, then the line is said to be oblique to the plane.
Plan Containing LinePlan Containing LineWhen all the points of the line belong to the plane is because the line is contained in the plane. So, she is "part of the plan". In some textbooks the line is also called coincident with the plane.

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