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.
Need flash cards for quick review? Quizlet flashcards on points, lines and planes postulates and theorems