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