introduction to geometry: points, lines, and planes
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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…
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