Post on 24-May-2015
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AnglesAngles
You will learn to name and identify parts of an angle.
1) Opposite Rays2) Straight Angle3) Angle4) Vertex5) Sides6) Interior7) Exterior
AnglesAngles
___________ are two rays that are part of a the same line and have only theirendpoints in common.
AnglesAngles
___________ are two rays that are part of a the same line and have only theirendpoints in common.Opposite rays
AnglesAngles
___________ are two rays that are part of a the same line and have only theirendpoints in common.Opposite rays
XY Z
XY and XZ are ____________.
AnglesAngles
___________ are two rays that are part of a the same line and have only theirendpoints in common.Opposite rays
XY Z
XY and XZ are ____________.opposite rays
AnglesAngles
___________ are two rays that are part of a the same line and have only theirendpoints in common.Opposite rays
XY Z
XY and XZ are ____________.opposite rays
The figure formed by opposite rays is also referred to as a ____________.
AnglesAngles
___________ are two rays that are part of a the same line and have only theirendpoints in common.Opposite rays
XY Z
XY and XZ are ____________.opposite rays
The figure formed by opposite rays is also referred to as a ____________.straight angle
AnglesAngles
There is another case where two rays can have a common endpoint.
R
S
T
This figure is called an _____.
AnglesAngles
There is another case where two rays can have a common endpoint.
R
S
T
This figure is called an _____.angle
AnglesAngles
There is another case where two rays can have a common endpoint.
R
S
T
This figure is called an _____.angle
Some parts of angles have special names.
The common endpoint is called the ______,
AnglesAngles
There is another case where two rays can have a common endpoint.
R
S
T
This figure is called an _____.angle
Some parts of angles have special names.
The common endpoint is called the ______,vertex
AnglesAngles
There is another case where two rays can have a common endpoint.
R
S
T
This figure is called an _____.angle
Some parts of angles have special names.
The common endpoint is called the ______,vertex
vertex
and the two rays that make up the sides ofthe angle are called the sides of the angle.
side
side
AnglesAngles
Definitionof Angle
An angle is a figure formed by two noncollinear rays that have a common endpoint.
E
D
F
2
Symbols: DEF
AnglesAngles
Definitionof Angle
An angle is a figure formed by two noncollinear rays that have a common endpoint.
E
D
F
2
Symbols: DEF
FED
AnglesAngles
Definitionof Angle
An angle is a figure formed by two noncollinear rays that have a common endpoint.
E
D
F
2
Symbols: DEF
E
FED
AnglesAngles
Definitionof Angle
An angle is a figure formed by two noncollinear rays that have a common endpoint.
E
D
F
2
Symbols: DEF
2
E
FED
AnglesAngles
B
A
1
C
1) Name the angle in four ways.
AnglesAngles
B
A
1
C
1) Name the angle in four ways.
ABC
AnglesAngles
B
A
1
C
1) Name the angle in four ways.
ABC
CBA
AnglesAngles
B
A
1
C
1) Name the angle in four ways.
ABC
CBA
AnglesAngles
B
A
1
C
1) Name the angle in four ways.
ABC
B
CBA
AnglesAngles
B
A
1
C
1) Name the angle in four ways.
ABC
1
B
CBA
AnglesAngles
B
A
1
C
1) Name the angle in four ways.
ABC
1
B
CBA
2) Identify the vertex and sides of this angle.
AnglesAngles
B
A
1
C
1) Name the angle in four ways.
ABC
1
B
CBA
2) Identify the vertex and sides of this angle.
Point Bvertex:
AnglesAngles
B
A
1
C
1) Name the angle in four ways.
ABC
1
B
CBA
2) Identify the vertex and sides of this angle.
Point B
BA and BC
vertex:
sides:
AnglesAngles
W
Y
X1) Name all angles having W as their vertex.
Z
1
2
AnglesAngles
W
Y
X1) Name all angles having W as their vertex.
1
Z
1
2
AnglesAngles
W
Y
X1) Name all angles having W as their vertex.
1
2
Z
1
2
AnglesAngles
W
Y
X1) Name all angles having W as their vertex.
1
2
Z
1
2XWZ
AnglesAngles
W
Y
X1) Name all angles having W as their vertex.
1
2
Z
1
2
2) What are other names for ?1
XWZ
AnglesAngles
W
Y
X1) Name all angles having W as their vertex.
1
2
Z
1
2
2) What are other names for ?1
XWY or YWX
XWZ
AnglesAngles
W
Y
X1) Name all angles having W as their vertex.
1
2
Z
1
2
2) What are other names for ?1
XWY or YWX
3) Is there an angle that can be named ? W
XWZ
AnglesAngles
W
Y
X1) Name all angles having W as their vertex.
1
2
Z
1
2
2) What are other names for ?1
XWY or YWX
3) Is there an angle that can be named ? W
No!
XWZ
AnglesAngles
An angle separates a plane into three parts:
1) the ______
W
Y
Z
A
B
AnglesAngles
An angle separates a plane into three parts:
1) the ______interior
interior
W
Y
Z
A
B
AnglesAngles
An angle separates a plane into three parts:
1) the ______
2) the ______
interior
A
Binterior
W
Y
Z
AnglesAngles
An angle separates a plane into three parts:
1) the ______
2) the ______
interior
exterior
exterior
interior
W
Y
Z
A
B
AnglesAngles
An angle separates a plane into three parts:
1) the ______
2) the ______
3) the _________
interior
exterior
exterior
interior
W
Y
Z
A
B
AnglesAngles
An angle separates a plane into three parts:
1) the ______
2) the ______
3) the _________
interior
exterior
angle itself
exterior
interior
W
Y
Z
A
B
AnglesAngles
An angle separates a plane into three parts:
1) the ______
2) the ______
3) the _________
interior
exterior
angle itself
exterior
interior
W
Y
Z
A
B
In the figure shown, point B and all other points in the blue region are in the interiorof the angle.
AnglesAngles
An angle separates a plane into three parts:
1) the ______
2) the ______
3) the _________
interior
exterior
angle itself
exterior
interior
W
Y
Z
A
B
In the figure shown, point B and all other points in the blue region are in the interiorof the angle.
Point A and all other points in the greenregion are in the exterior of the angle.
AnglesAngles
An angle separates a plane into three parts:
1) the ______
2) the ______
3) the _________
interior
exterior
angle itself
exterior
interior
W
Y
Z
A
B
In the figure shown, point B and all other points in the blue region are in the interiorof the angle.
Point A and all other points in the greenregion are in the exterior of the angle.
Points Y, W, and Z are on the angle.
AnglesAngles
B
Is point B in the interior of the angle, exterior of the angle, or on the angle?
G
P
AnglesAngles
B
Is point B in the interior of the angle, exterior of the angle, or on the angle?
ExteriorG
P
AnglesAngles
B
Is point B in the interior of the angle, exterior of the angle, or on the angle?
ExteriorG
Is point G in the interior of the angle, exterior of the angle, or on the angle?
P
AnglesAngles
B
Is point B in the interior of the angle, exterior of the angle, or on the angle?
ExteriorG
Is point G in the interior of the angle, exterior of the angle, or on the angle?
On the angle
P
AnglesAngles
B
Is point B in the interior of the angle, exterior of the angle, or on the angle?
ExteriorG
Is point G in the interior of the angle, exterior of the angle, or on the angle?
On the angle
Is point P in the interior of the angle, exterior of the angle, or on the angle?
P
AnglesAngles
B
Is point B in the interior of the angle, exterior of the angle, or on the angle?
ExteriorG
Is point G in the interior of the angle, exterior of the angle, or on the angle?
On the angle
Is point P in the interior of the angle, exterior of the angle, or on the angle?
Interior
P
§3.7 Perpendicular Lines§3.7 Perpendicular Lines