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…