Mathematics: Geometry - Lines and Planes

Points and Lines
A point is a fixed location in space, has no size or dimensions, and is commonly represented by a dot. A line is a set of points that extends infinitely in two opposite directions. It has length, but no width or depth. A line can be defined by any two distinct points that it contains. A line segment is a portion of a line that has definite endpoints. A ray is a portion of a line that extends from a single point on that line in one direction along the line. It has a definite beginning, but no ending.

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Interactions between Lines
Intersecting lines are lines that have exactly one point in common. Concurrent lines are multiple lines that intersect at a single point. Perpendicular lines are lines that intersect at right angles.

They are represented by the symbol
.

The shortest distance from a line to a point not on the line is a perpendicular segment from the point to the line. Parallel lines are lines in the same plane that have no points in common and never meet. It is possible for lines to be in different planes, have no points in common, and never meet, but they are not parallel because they are in different planes.

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A transversal is a line that intersects at least two other lines, which may or may not be parallel to one another. A transversal that intersects parallel lines is a common occurrence in geometry. A bisector is a line or line segment that divides another line segment into two equal lengths. A perpendicular bisector of a line segment is composed of points that are equidistant from the endpoints of the segment it is dividing.

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Bisector -

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The projection of a point on a line is the point at which a perpendicular line drawn from the given point to the given line intersects the line.  This is also the shortest distance from the given point to the line. The projection of a segment on a line is a segment whose endpoints are the points formed when perpendicular lines are drawn from the endpoints of the given segment to the given line. 
This is similar to the length a diagonal line appears to be when viewed from above.

Projection of a point on a line -

Projection of a segment on a line -


Planes
A plane is a two-dimensional flat surface defined by three non-collinear points. A plane extends an infinite distance in all directions in those two dimensions. It contains an infinite number of points, parallel lines and segments, intersecting lines and segments, as well as parallel or intersecting rays. A plane will never contain a three-dimensional figure or skew lines, lines that don't intersect and are not parallel. Two given planes are either parallel or they intersect at a line.

A plane may intersect a circular conic surface to form conic sections, such as a parabola, hyperbola, circle or ellipse.