Download Module 2 Lesson 1 Angles

Module 2
Lesson 1
Angles
Ray
• A portion of a line that starts at one point
and extends indefinitely in one direction
C
A
B
• Name: must be named using the endpoint
FIRST, then another point on the ray
• Symbol: a ray drawn above the name
AB
NOT BA or AC
Opposite Rays
• Two rays that have the same starting point
but extend in opposite directions.
Y
X
XZ and XY are opposite rays
• Form a line and straight angle.
Z
Angles
• Made of two rays that have a common
endpoint
• The rays are considered the sides of the
angle.
• The common endpoint is considered the
vertex of the angle.
A
Sides: BA, BC
Vertex: point B
B
C
Naming an Angle
• An angle can be named in three different
ways
1. Using the vertex (can only have one angle
with that vertex)
B
2. Using three different points
(vertex must be in the middle)
ABC or CBA
3. Using a number
B
1
A
1
C
Types of Angles
1. Acute Angle – an angle that measures
between 0° and 90°.
2. Right Angle – an angle that measures
exactly 90°.
3. Obtuse Angle – an angle that measures
between 90° and 180°.
4. Straight Angle – an angle that measures
exactly 180°.
You try…Identify the type of angle shown.
1.
2.
3.
4.
Adjacent Angles
• Adjacent angles are two angles that share
a vertex and have one side in common.
DGE is adjacent to EGF
E
D
Vertex: point G
Common side: GE
F
G
Vertical Angles
• Vertical angles are two angles created by
interesting lines. Share a vertex and have
no interior points in common.
Vertex: point M
HML is vertical to JMK
HMJ is vertical to LMK
J
H
M
K
L
Vertical angles are always CONGRUENT.
Linear Pair
• A linear pair is two angles that share a
vertex, have a common side, and their non
common sides are opposite rays.
Vertex: point N
NP and NM are opposite rays.
MNO and ONP are a linear pair.
O
M
N
P
Linear pairs always have a sum of 180°.
Complementary Angles
• Complementary angles are two angles
that have a sum of 90°.
Picture 1
Picture 2
67
50
23
40
Complementary Angles can be adjacent or nonadjacent.
Two angles are complements of each other if they are
complementary.
Supplementary Angles
• Supplementary angles are two angles that
have a sum of 180°.
Picture 1
Picture 2
58
115
65
122
Supplementary angles can be adjacent or nonadjacent.
Two angles are supplements of each other if they are
supplementary.
Perpendicular Angles
• Perpendicular angles are angles that are
formed by perpendicular lines.
• Each angle will always have a measure of
90°.
If there is one right angle, then there are a total of four right angles.
You try…Give the most specific angle pair for angles 1
and 2.
1.
2.
2
1
3.
1
2
4.
2
1
1
5.
2
1
2
You try….Find the measure of angle 1.
1.
2.
k
nk
1
n
1
124
3.
4.
36
1
62
1
You try….
Find the value of x.
1.
ab
2.
5x + 2
7x - 1
6x
Find the value of the angle indicated.
3.
4.
Find mNQP.
Find mCBD.
O
B
A
N
6x + 10
4x + 10
7x - 11
P
Q
M
D
9x + 5
C
Answers to You Try Slides
Identify the type of angle shown
1. straight
2. obtuse
3. right
4. acute
Give the most specific angle pair for angles 1 and 2.
1. complementary
2. adjacent
3. linear pair or supplementary
4. vertical
5. perpendicular angles
Find the measure of angle 1.
1. 124°
2. 90°
Find the value of x.
1. 13
2. 8
Find the value of the angle indicated.
3. 38°
4. 104°
3. 144°
4. 28°