geometry vocabulary basic geometry concepts. example of how notes should look...
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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.
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