Introduction to Geometry: Points, Lines, and Planes
14
Introduction to Geometry: Points, Lines, and Planes
description
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. - PowerPoint PPT Presentation
Transcript of 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.– Lots of new vocabulary terms, symbols,
and rules.
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.
Essential Vocabulary
These are terms you must be most familiar with, as they will be an integral part of the course.
PointNo size or dimension, merely position.
PWritten as: P
Written using a single, capital letter. Points are equidistant, if they are the same measurable distance away from a given location.
LineContains infinitely many points
extending in opposite directions.
A Bh
C
Written as:
Any two points name the line,
order does NOT matter.
PlaneAn imaginary, perfectly flat surface with no thickness that extends endlessly in all
directions.
MWritten as: M
Plane can be named using a single capitalletter OR using three or four points.Ex. Plane M or Plane ABC or ABC
Collinear PointsPoints that lie on the same line.
A B C
A, B, and C are collinear points.
Noncollinear Points
Points that do not lie on the same line.
Ex. P and R are noncollinear points.
Ex. S and P are noncollinear points.
P Q
R
S
Coplanar PointsPoints that lie on the same plane.
M NP
P, M, and N are coplanar points.
Noncoplanar Points
Points that do not lie on the same plane.
B M
A
N A, B, M, and N are noncoplanar points. A
B C
DE
IntersectionThe set of points that lie in both
figures.
R
R is the intersection of the two lines.
Diagram
A
B C
DE
D
A B
C
E F
G
Use the diagram to answer the following.
• 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.
Questions…
