Download Geometry Notes - Net Start Class

1.1 Understanding Points, Lines and Planes
Definition:
A basic figure that is not
defined in terms of other
figures
Facts/Characteristics:
Foundations for all other
Geometry terms; zero-, one-,
and two-dimensional
representations
Non-Example:
Example:
Point A
Line
Plane A
Definition:
Facts/Characteristics:
An undefined term in
Geometry
Non-Example:
B
Example:
B
Anything that has a definition
B
R
A
B
R
C
Facts/Characteristics:
A straight path that has no
thickness and extends forever
Notation:
Non-Example:
B
Definition:
An undefined term
in Geometry
AB
Example:
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A
A
Definition:
An undefined term
in Geometry
A
Names a location and has no size
Named with a capital letter
B
A
R
B
C
R
A flat surface that has no thickness
and extends forever
Notation: Plane R or Plane ABC
Non-Example:
A
C
C
Facts/Characteristics:
Example:
A
A
A
A
B
Definition:
Facts/Characteristics:
Points that lie on the
same line
2 Points are ALWAYS collinear
Non-Example:
Example:
Definition:
A part of a line
consisting of two
endpoints and all points
between them
Non-Example:
Example:
B
A
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Facts/Characteristics:
Notation: “Segment AB” or
“ AB ”
AB (with no notation) refers to
a segment’s length
Definition:
Points that lie in the
same plane
Example:
Definition:
A point at an end of a
segment or the starting
point of a ray
Example:
Facts/Characteristics:
3 Points are ALWAYS
coplanar
Non-Example:
Facts/Characteristics:
ItIt’s
is labeled
a point
with
a a
a Point,like
so it’s
named
with
capital
letter.
It
is
located
at
both
single capital letter.
ends of a segment and at one end
of a ray
Non-Example:
Definition:
A part of a line that
starts at an endpoint
and extends forever in
one direction
Facts/Characteristics:
Notation: “Ray AB” or AB
The first letter is always the
endpoint. The second letter is any
other point on the ray
Non-Example:
Example:
Definition:
Two rays that have a
common endpoint and
form a line
Example:
Facts/Characteristics:
Forms a straight angle (180o)
Non-Example:
B
A
Definition:
A statement that is
accepted as true
without proof
Example:
Through any two points there is
exactly one line.
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Facts/Characteristics:
Also called an Axiom
Non-Example:
A definition:
Segment – A part of a line with
two endpoints and all points
between them
Definition:
A plane that is divided
into four regions by a
horizontal line called
the x-axis and a vertical
line called the y-axis
Example:
Facts/Characteristics:
A 2-Dimensional
figure used to represent
points and figures with
distinct locations.
Non-Example:
A number line
Undefined
Term
Collinear
Coordinate
Plane
Segment
Midpoint
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Point
Congruent
Segments
Coplanar
Ray
Opposite
Rays
Between
Construction
Bisect
Coordinate
Distance
Endpoint
Length
Line
Plane
Postulate
1.2 Measuring and Constructing Segments
Definition:
A number(s) used to identify
the location of a point.
Facts/Characteristics:
Number Line – 1 number used
Coordinate grid – 2 numbers used
In space – 3 numbers used
Non-Example:
Example:
A=2
1
Definition:
A numerical measurement in
One-Dimension
Often used in place of the word
“Distance”
Measured w/ a
ruler
Non-Example:
Area =
1
in
4
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bh
2
h
b
How far from one point to
another along a line.
Often referred to as “LENGTH”
Non-Example:
Example:
Distance from Z to Y is 8 units
(So the length of segment ZY is
8 units)
Facts/Characteristics:
Example:
Facts/Characteristics:
Area =
2
A slope: 
3
B = (-2, 3)
Definition:
The distance between two
endpoints of a segment
Definition:
The absolute value of the
difference of the coordinates
of the points
Two segments that
have the same length
Example:
bh
2
h
b
Facts/Characteristics:
Same length. Marked with tick
marks on the segment.
Non-Example:
Just because they look
congruent doesn’t
mean they are. They
MUST have congruent
markings
Definition:
A method of creating a
figure that is considered
to be mathematically
precise
Facts/Characteristics:
3 methods:
Compass/Starightedge
Geometry Software
Paper Folding
Definition:
Given three points A, B, and
C, B is between A and C if
and only if all three of the
points lie on the same line
and AB + BC = AC
Non-Example:
Example:
Facts/Characteristics:
Points are collinear
Non-Example:
Example:
B
Drawing uses
measurement,
Construction
Doesn’t
Definition:
The point that divides a
segment into two congruent
segments
Non-Example:
A
B
B
C
C
A
Facts/Characteristics:
Midpoint is equally distant from
the two endpoints.
Must mark the two new segments
congruent
Example:
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A
Definition:
To divide into two
congruent parts
Example:
C
100
= 50
2
Facts/Characteristics:
You can bisect segments,
angles, numbers, anything. It
just means to cut in half.
Non-Example:
50 + 50 = 100
Adding together
Definition:
A line, ray, or segment that
divides a segment into two
congruent segments
Facts/Characteristics:
Bisector must pass through the
midpoint.
Non-Example:
Example:
Definition:
The side opposite the right angle
in a right triangle
Example:
Hypotenuse
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Segment
Bisector
Always the longest side in right
triangle
Non-Example:
Hypotenuse
Ray
Facts/Characteristics:
Bisect
Longest side but
not a hypotenuse
Leg of a Right
Triangle
1.3 Measuring and Constructing Angles
Definition:
A figure formed by two
rays with a common
endpoint
Non-Example:
Example:
A
B
Facts/Characteristics:
Notation:  ABC or  CBA or
B
Definition:
The common endpoint
of the sides of the angle
Example:
Facts/Characteristics:
It’s a Point and named with one
capital letter
Used with 2-dimensional
polygons and 3-dimensional
solids
Non-Example:
C
Definition:
The set of all points between
the sides of an angle
Example:
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Facts/Characteristics:
Infinite number of points
Not including points ON the angle
Non-Example:
Definition:
The set of all points outside an
angle
Example:
Facts/Characteristics:
Infinite number of points
Not including points ON the angle
Non-Example:
Definition:
Smallest amount of rotation
about a vertex from one ray to
another.
Facts/Characteristics:
An angle is measured in degrees
Angles are measured with a
protractor
(Length of ray does not
determine angle
measure)
Non-Example:
Example:
Definition:
Two angles whose measures
have a sum of 180o
Non-Example:
Example:
Length:
37o
3 cm
Definition:
An angle that measures greater
than 0o and less than 900
Example:
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Facts/Characteristics:
Angles may or may not be
adjacent
Facts/Characteristics:
One of the 4 types of angles
89.99999o, but not 90o
Non-Example:
o
140
o
40
Definition:
An angle that measures 90o
Example:
53o
Facts/Characteristics:
One of the 4 types of angles.
Must measure EXACTLY 90o
Non-Example:
Definition:
An angle that measures greater
than 90o and less than 180o
Facts/Characteristics:
One of the 4 types of angles
Can be 90.111111o or even
179.9999999o or anything in
between
Non-Example:
Example:
Definition:
Angles that have the same
measure
Facts/Characteristics:
Equal amount of rotation
between rays
Notation:  A   B
Non-Example:
Example:
A
B
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Definition:
Facts/Characteristics:
A 180o angle
One of the 4 types of angles.
Forms a straight line.
Formed by opposite rays
Example:
Definition:
A ray that divides and angle into
two congruent angles
Example:
Non-Example:
Facts/Characteristics:
The two new congruent angles
are adjacent
Non-Example:
1.4 Pairs of Angles
Definition:
Two angles in the same plane
with a common vertex and a
common side, but no common
interior points
Example:
Facts/Characteristics:
Share a common ray
Have no specific angle measure
they are supposed to add up to.
Non-Example:
Definition:
A pair of adjacent angles whose
noncommon sides are opposite
rays
The angles are adjacent and
supplementary
Non-Example:
Example:
135o 45o
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Facts/Characteristics:
135o
45o
Definition:
Facts/Characteristics:
Two angles whose measures have Can be adjacent or not adjacent
a sum of 90o
Definition:
A unit of measure of an angle
Facts/Characteristics:
One degree is
1
of a
360
circle
Non-Example:
Example:
37o
53o
37o
140o
40o
Definition:
Facts/Characteristics:
The nonadjacent angles formed
by two intersecting lines
Congruent Angles
Non-Example:
Example:
2
Example:
1
1
2
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Definition:
Example:
Non-Example:
Inches, Feet, Yards,
Meters, Liters, Grams
Facts/Characteristics:
Non-Example:
Definition:
Facts/Characteristics:
Non-Example:
Example:
Angle
Measure of
an Angle
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Vertex
Supplementary
Angles
Definition:
Facts/Characteristics:
Non-Example:
Example:
Interior of
an Angle
Acute Angle
Exterior of
an Angle
Right
Angle
Obtuse
Angle
Adjacent
Angles
Vertical
Angles
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Straight
Angle
Linear
Pair
Congruent
Angles
Complementary
Angles
Angle
Bisector
Degree
Leg
Midpoint
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Opposite
Rays
Length
Plane
Line
Postulate