Transcript Pairs of Angles - St. Landry Parish School Board

Pairs of
Angles
Angles – sides and vertex
angle
This figure is called an _____.
Some parts of angles have special names.
S
The common endpoint is called
vertex
the ______,
and the two rays that make up
the sides of the angle are called
the sides of the angle.
R
vertex
side
T
Naming Angles
There are several ways to name this angle.
1) Use the vertex and a point from each side.
SRT
or
S
TRS
The vertex letter is always in the middle.
2) Use the vertex only.
R
side
R
If there is only one angle at a vertex, then the
angle can be named with that vertex.
3) Use a number.
1
1
vertex
T
Angles Review
1) Name the angle in four ways.
ABC
C
A
CBA
B
1
1
B
2) Identify the vertex and sides of this angle.
vertex: Point B
sides:
BA
and
BC
Angle Classification
Once the measure of an angle is known, the angle
can be classified as one of three types of angles.
These types are defined in relation to a right angle.
Types of Angles
A
obtuse angle
Greater than 90°
A
A
right angle
Equal to 90 °
acute angle
Less than 90 °
Angle Classification
Classify each angle as acute, obtuse, or right.
110°
40°
90°
Obtuse
Right
Acute
50°
130°
Acute
Obtuse
75°
Acute
Straight Angles
Opposite
rays are two rays that are part of the
___________
same line and have only their endpoints in
common.
X
Z
Y
opposite rays
XY and XZ are ____________.
The figure formed by opposite rays is also
referred to as a ____________.
straight angle A straight
angle measures 180 degrees.
Adjacent Angles
When you “split” an angle, you create two angles.
The two angles are called
adjacent angles
_____________
adjacent = next to, joining.
B
A
2
1
1 and 2 are examples of adjacent
angles. They share a common ray.
C
Name the ray that 1 and 2 have in common. BD
Adjacent Angles
Determine whether 1 and 2 are adjacent angles.
No. They have a common vertex B, but
no
common side
_____________
2
1
B
1
G
Yes. They have the same vertex G and a
common side with no interior points in
common.
2
N
J
L
2
1
No. They do not have a common vertex or
a____________
common side
The side of 1 is
LN
The side of 2 is JN
Complementary Angles
Two angles are complementary if and
only if The sum of their degree measure
is 90.
A
E
Definition of
D
Complementary
Angles
B
30°
C
60°
F
mABC + mDEF = 30 + 60 = 90
Complementary Angles
Some examples of complementary angles are shown below.
15°
H
P
75°
mH + mI = 90
Q
40°
mPHQ + mQHS = 90
50°
H
S
U
T
I
60°
V
mTZU + mVZW = 90
30°
Z
W
Supplementary Angles
If the sum of the measure of two angles is 180, they form a
special pair of angles called supplementary angles.
Two angles are supplementary if and only if the
sum of their degree measure is 180.
Definition
of
Supplementary
Angles
D
C
50°
A
130°
B
E
F
mABC + mDEF = 50 + 130 = 180
Supplementary Angles
Examples of supplementary angles are shown below.
75°
H
I
mH + mI = 180
105°
Q
130°
50°
H
P
S
U
V
60°
120°
60°
Z
T
mPHQ + mQHS = 180
mTZU + mUZV = 180
and
mTZU + mVZW = 180
W
Vertical Angles
When two lines intersect, ____
four angles are formed.
There are two pair of nonadjacent angles.
These pairs are called _____________.
vertical angles
4
1
3
2
Vertical Angles
Two angles are vertical if and only if they
are two nonadjacent angles formed by a
pair of intersecting lines.
Definition
of
Vertical angles:
Vertical
Angles
4
1
3
2
1 and 3
2 and 4
Vertical Angles
Vertical angles are congruent.
n
2
m
3
1
4
1  3
2  4
Vertical Angles
Find the value of x in the figure:
130°
x°
The angles are vertical angles.
So, the value of x is 130°.