Geometry Vocabulary

Basic Geometry Concepts

Example of How notes should look

Name____________________________

Date___________________Period_____

Geometry Vocabulary and Symbols

Unit 1

This side is for you to formulate questions at the end of class.

1. Conjecture1. Is an unproven statement that is

based on a pattern or statement

Geometry Vocabulary

Conjecture

is an unproven statement that is based on a pattern or statement

Inductive Reasoning

is when you look for patterns and make conjectures

Geometry Vocabulary

Counterexample

is an example that shows a conjecture is false

EX:

Statement: All birds can fly

Counterexample: Penguin

Geometry Vocabulary

Undefined terms:

these are terms that cannot be mathematically defined using other known words

We must describe Point, Line, and Plane instead of defining them.

Geometry Vocabulary

Point:Has NO dimensionIt is represented by a small dot

A

Point A

Geometry Vocabulary

Line:Has ONE dimensionIt extends without end in two

directionsIt is represented by a line with two

arrowheads

LINE

A

B

l

Name this line

ABOR

Line l

Geometry Vocabulary

Line:NOTE: For every two points there can be exactly one line formed

Geometry Vocabulary

Plane:Has TWO dimensionsIt is represented by a shape that

looks like a floor or a wallYou have to imagine that it

extends without end in all directions.

PLANE

DE

F

m

Name Plane

Plane DEF

OR

Plane m

Geometry Vocabulary

Plane:NOTE: For every three non collinear points there exists one plane.

Geometry Vocabulary

Space

is a set of all points

Postulates

Are statements that are acepted without further justification. This is a statement of fact

Geometry Vocabulary

Congruent

means the figures are exactly the same

Geometry Vocabulary

Collinear points

Points that lie on the same line

Non Collinear points

Are points that do not lie on the same line.

Coplanar

Points and lines in the same plane

Ex. 1: Naming Collinear Points

a. Name three points that are collinear

Solution: D, E and F lie on the

same line, so they are collinear.

G

D E F

H

Ex. 2: Naming Coplanar Points

b. Name four points that are coplanar.

Solution:

D, E, F, and G lie on the same plane, so they are coplanar. Also D, E, F, and H are coplanar; although, the plane containing them is not drawn.

G

D E F

H

Ex. 3: Naming Non Collinear Points

c. Name three points that are not collinear.

Solution: There are many

correct answers. For instance, points H, E, and G do not lie on the same line.

G

D E F

H

Geometry Vocabulary

Segment-

Is the part of the line consisting of two endpoints.

A B

Segment AB

Geometry Vocabulary

Ray-

Is the part of the line consisting of one endpoint and all the points of the line on one side of the endpoint.

Ray AB

A B

Note that AB is the same as BA and AB is the same as BA. However, AB and BA are not the same. They have different initial points and extend in different directions.

A B

If C is between A and B, then CA and CB are opposite rays.

Like points, segments and rays are collinear if they lie on the same line. So, any two opposite rays are collinear. Segments, rays and lines are coplanar if they lie on the same plane.

A BC

Ex. 4: Opposite Rays

Draw two lines. Label points on the lines and name two pairs of opposite rays.

Solution: Points P, Q, and

X are collinear and X is

between P and Q. So

XP and XQ are

opposite rays.

P

MQ

N

X

Geometry Vocabulary

Intersection

The term intersect is used when lines, rays, line segments or figures meet, that is, they share a common point or points. The point or points they share is called the point of intersection. We say that these figures intersect.

Intersecting Lines

If two lines intersect then they intersect in exactly one point.

Line intersecting plane

If a line intersects with a plane then it intersect in exactly one point.

Plane intersecting Plane

If two planes intersect than they intersect at a line

Geometry Vocabulary

Parallel Lines

Are coplanar lines that do NOT intersect

Geometry Vocabulary

Skew Lines

Are noncoplanar lines; therefore they are NOT parallel and do not intersect

Geometry Vocabulary

Perpendicular Lines

Are two lines that intersect to form right (90°) angle.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.