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Module 2
Lesson 1
Angles
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Slide 1
Notes:
Module 2
Lesson 1
Angles
Module 2
Lesson 1
Angles
Duration: 00:00:09
Advance mode: Auto
Slide 2
Ray
Duration: 00:00:32
Advance mode: Auto
In this module, you will be introduced to angles
and constructions. In this lesson, you will be
introduced to what makes an angle and what
some special angle pairs are.
Ray
Notes:
• 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
A ray is a portion of a line that starts at one point
but extends indefinitely in one direction. So a ray
has a starting point, but no ending point. To
name a ray, you MUST use the starting point as
the start of the name. The second point can be
any point that is on the ray. The ray in the figure
would then be ray AB. Ray BA would be
incorrect because the ray does not start at B and
ray AC would be incorrect because C is in the
other direction of the ray.
NOT BA or AC
Slide 3
Opposite Rays
Duration: 00:00:23
Advance mode: Auto
Opposite Rays
Notes:
• Two rays that have the same starting point
but extend in opposite directions.
Y
X
XZ and XY are opposite rays
Z
Opposite rays are two rays that have the same
starting point but extend in opposite directions.
Opposite rays always form a line and a straight
angle. In the diagram, ray XZ and ray XY are
opposite rays. They share a starting point of X
but ray XY extends to the left and ray XZ extends
to the right.
• Form a line and straight angle.
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Slide 4
Angles
Duration: 00:00:24
Advance mode: Auto
Notes:
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
An angle is a geometric figure that is formed by
two rays. These rays will have a common
endpoint, that endpoint will be known as the
vertex of the angle. The vertex gives the location
of the angle. The two rays will be the sides of
the angle. The angle pictured has a vertex at
point B and the sides of the angle will be ray BA
and ray BC.
B
C
Slide 5
Naming an Angle
Duration: 00:00:33
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Naming an Angle
Notes:
• 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
Slide 6
Types of Angles
Duration: 00:00:35
Advance mode: Auto
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 .
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Angles can be named in three different ways.
Way one is to use the vertex point. The angle
would be called angle B. This way can only be
used when there is only one angle with that
vertex. Way two is to use three different points.
The vertex must be the middle point in the name.
The angle would be called angle ABC or angle
CBA. Both have point B in the middle. Way
three is to use a number given in the diagram.
The angle would be called angle 1.
Notes:
There are four different types of angles. The
smallest is an acute angle. An acute angle
measures more than 0 degrees but less than 90
degrees. The second type is a right angle. A
right angle measure exactly 90 degrees. Right
angles will be marked with a box at the vertex of
the angle. The third type is an obtuse angle. An
obtuse angle measures more than 90 degrees
but less than 180 degrees. The fourth type is a
straight angle. A straight angle measures
exactly 180 degrees.
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Slide 7
You try...
You try…Identify the type of angle shown.
1.
2.
Duration: 00:00:06
Advance mode: By user
3.
Duration: 00:00:21
Advance mode: Auto
You try these examples. See the last slide in the
presentation to check your answers.
4.
Slide 8
Adjacent Angles
Notes:
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
Notes:
Adjacent angles are a set of two angles that
share a vertex and have a common side.
Adjacent angles also have no interior points in
common. Point G would be the vertex to both
angles and the common side would be ray GE.
Angle DGE would be adjacent to angle EGF.
Common side: GE
F
G
Slide 9
Vertical Angles
Vertical Angles
Duration: 00:00:32
Advance mode: Auto
• 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.
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Notes:
Vertical angles are a set of angles that are
created by two intersecting lines. Vertical angles
share a vertex but nothing else. With each set of
intersecting lines, there will be two different sets
of vertical angles. Angle HML would be vertical
to angle JMK. Angle HMJ would be vertical to
angle LMK. One thing to remember about
vertical angles is that they will always be
congruent. Remember that congruent means
that they have the same measure.
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Slide 10
Linear Pair
Linear Pair
Duration: 00:00:33
Advance mode: Auto
Notes:
• 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
P
N
Linear pairs are two angles that share a vertex
and a common side. Their non common sides
form opposite rays. Remember that opposite
rays are two rays that have the same starting
point and extend in opposite directions. Point N
would be the vertex of both angles. Ray NP and
ray NM would be opposite rays. Angle MNO and
angle ONP would be a linear pair. Linear pairs
will always have a sum of 180°.
Linear pairs always have a sum of 180 .
Slide 11
Complementary Angles
Duration: 00:00:16
Advance mode: Auto
Complementary Angles
Notes:
Complementary angles are a pair of angles that
when added together will equal 90°.
Complementary angles may be adjacent, making
a right angle, like in picture 1, or complementary
angles many be nonadjacent, like in picture 2.
• Complementary angles are two angles
that have a sum of 90 .
Picture 2
Picture 1
67
50
23
40
Complementary Angles can be adjacent or nonadjacent.
Slide 12
Supplementary Angles
Duration: 00:00:16
Advance mode: Auto
Notes:
Supplementary Angles
• Supplementary angles are two angles that
have a sum of 180 .
Picture 1
Picture 2
Supplementary angles are a pair of angles that
when added together will equal 180°.
Supplementary angles may be adjacent, making
a linear pair, like in picture 1, or supplementary
angles may be nonadjacent, like in picture 2.
58
115
65
122
Supplementary angles can be adjacent or nonadjacent.
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Slide 13
Perpendicular Angles
Perpendicular Angles
Duration: 00:00:19
Advance mode: Auto
• Perpendicular angles are angles that are
formed by perpendicular lines.
• Each angle will always have a measure of
90 .
Notes:
Perpendicular angles are angles that are formed
by perpendicular lines. These angles are always
right angles, therefore they will always have a
measure of 90°. An important fact to know is
that if there is one right angle pictured, then their
will be a total of four right angles in the figure.
If there is one right angle, then there are a total of four right angles.
Slide 14
You try...
Duration: 00:00:06
Advance mode: By user
You try…Give the most specific angle pair for angles 1
and 2.
Notes:
1.
You try these examples. See the last slide in the
presentation to check your answers.
2.
2
1
1
3.
2
4.
2
1
1
2
1
5.
2
Slide 15
You try...
You try….Find the measure of angle 1.
1.
2.
Notes:
k
nk
Duration: 00:00:06
Advance mode: By user
1
n
1
124
3.
4.
36
You try these examples. See the last slide in the
presentation to check your answers.
62 
1
1
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Slide 16
You try...
Duration: 00:00:06
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You try….
Find the value of x.
1.
ab
Notes:
You try these examples. See the last slide in the
presentation to check your answers.
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
Q
M
C
9x + 5
D
P
Slide 17
Answers to You Try Slides
Duration: 00:00:10
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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
3. 144°
Notes:
Here are the answers to each of the you try
slides. I hope you did well. After you have
completed this presentation, proceed with the
Check Your Understanding activity.
4. 28°
2. 8
Find the value of the angle indicated.
3. 38°
4. 104°
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