Plane Geometry – point, line and plane

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.

Links

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

• Author
• Recent Posts

Aniruddha Pochimcherla

As a high school senior and co-founder of STEAMism and TimeforAI.com, Ani enjoys challenges and problem solving, technical subjects including Artificial Intelligence and Engineering Design, and collaborating with like-minded peers on events and hackathons. He has interned with the City of Austin, was a NASA High School Aerospace Scholar in 2019-2020 and is a Math tutor at Mathnasium. He has been blogging since 2nd grade and dabbles in web design and coding. He enjoys STEM subjects and teaching, so STEAMism is a great way for him to combine both.

Latest posts by Aniruddha Pochimcherla (see all)

• An Interview with the Co-Founders of Dermanostix - August 14, 2020
• NASA & SpaceX’s Successful Space Launch - June 12, 2020
• Types of Engineering - June 10, 2020