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Introduction to Geometry: Points, Lines, and Planes

Introduction to Geometry: Points, Lines, and Planes. Introduction to Geometry. This course will be much different from any other math class you have had before, it is much less about numbers and more about words. Geometry will be like learning a new language.

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Introduction to Geometry: Points, Lines, and Planes

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  1. Introduction to Geometry: Points, Lines, and Planes

  2. Introduction to Geometry • This course will be much different from any other math class you have had before, it is much less about numbers and more about words. • Geometry will be like learning a new language. • Lots of new vocabulary terms, symbols, and rules.

  3. The Rules • Postulates - statements that are accepted without any proof. • Axioms - statements accepted without proof necessary - usually related to a postulate. • Theorems - statements that can be proven using definitions, postulates, and axioms. • Corollaries - an additional part of a theorem.

  4. Essential Vocabulary These are terms you must be most familiar with, as they will be an integral part of the course.

  5. P Point Written as: P No size or dimension, merely position. Written using a single, capital letter. Points are equidistant, if they are the same measurable distance away from a given location.

  6. h A B C Written as: Line Contains infinitely many points extending in opposite directions. Any two points name the line, order does NOT matter.

  7. M Plane Written as:M An imaginary, perfectly flat surface with no thickness that extends endlessly in all directions. Plane can be named using a single capital letter OR using three or four points. Ex. Plane M or Plane ABC or ABC

  8. A B C Collinear Points Points that lie on the same line. A, B, and C are collinear points.

  9. R P Q S Noncollinear Points Ex. P and R are noncollinear points. Ex. S and P are noncollinear points. Points that do not lie on the same line.

  10. P M N Coplanar Points Points that lie on the same plane. P, M, and N are coplanar points.

  11. B C A E D N A B M Noncoplanar Points Points that do not lie on the same plane. A, B, M, and N are noncoplanar points.

  12. R Intersection The set of points that lie in both figures. R is the intersection of the two lines.

  13. F E B C D C E G D A A B Diagram Use the diagram to answer the following.

  14. Questions… • Are A, D, C, and F are coplanar ? • Are D, E, B, and G are coplanar ? • How many points are contained in Plane ABCD ? • Can a point be in more than one line ? • Name the intersection of Plane DEFC and Plane BGFC ? • Name two planes that do not intersect.

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