# Plane Geometry – point, line and plane

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### What is Plane Geometry?

Plane Geometry deals with flat 2-D (2 dimensional) shapes like lines, circles and triangles.

• Point:  is the most basic element of all geometric figures.  No dimension –> no length, no width, and no thickness. Describes the exact location or position on a surface or in space.
•  Line: is straight, has no thickness, has no ends –> extends in both directions indefinitely.
• Line segment: is straight, has no thickness, but ends at 2 distinct points.
• Ray: is straight, has no thickness, has one end point, and extends in one direction indefinitely.
• Plane: is a flat surface, has no end (extends indefinitely). Your wall or floor are examples of planes.

### Point, Line and Plane Postulates and Theorem

A theorem is a true statement that can be proven. A postulate or an axiom is a statement that is accepted as true without any proof.

#### Points and Lines:

• The 2 Point Postulate:  Through any two points there exists exactly one line.
• The Line-Point Postulate: A line contains at least two points.
• The Line Intersection Theorem: If two lines intersect, then they intersect in exactly one point.

#### Points and Planes:

• The 3 Point Postulate: Through any three non-collinear points, there exists exactly one plane.
• Plane-Point Postulate: A plane contains at least three non-collinear points.

#### Lines and Planes:

• Plane-Line Postulate: If two points lie in a plane, then the line containing them lies in the plane.
• Line Intersection Theorem: If two lines intersect, then exactly one plane contains both lines.
• Plane Intersection Postulate: If two planes intersect, then their intersection is a line.
• Point and Line contained in Plane Theorem: If a point lies outside a line, then exactly one plane contains both the line and the point.