Download 1.4: Measure and Classify Angles 1.5: Describe Angle

1.4: Measure and Classify Angles
1.5: Describe Angle Pair Relationships
Objectives:
1. To define, classify, draw, name, and
measure various angles
2. To use the Protractor and Angle Addition
Postulates
3. To use special angle relationships to find
angle measures
Magic Dough Revisited
Keeping in mind the
rules of working with
Magic Dough, create
an angle with your
dough. Don’t forget to
put the arrows and
points in the
appropriate places.
Angle
Vertex
A
Sides
B
C
• An angle consists of
two different rays
(sides) that share a
common endpoint
(vertex).
– Angle ABC, ABC,
or B
A “Rabbit Ear” antenna is a
physical model of an angle
Angle
• An angle consists of
two different rays
(sides) that share a
common endpoint
(vertex).
– Angle ABC, ABC,
or B
Example 1
How many angles can
be seen in the
diagram?
Name all the angles.
W
Y
X
Z
How Big is an Angle?
Is the angle between
the two hands of the
wristwatch smaller
than the angle
between the hands of
the large clock?
– Both clocks read 9:36
Click me to learn more
about measuring angles
Measure of an Angle
The measure of an angle is
the smallest amount of
rotation about the vertex
from one side to the other,
measured in degrees.
• Can be any value between
0 and 180
• Measured with a protractor
Classifying Angles
Create an example of each of these angles
with your Magic Dough.
How To Use a Protractor
The measure of this
angle is written:
mABC  34
Example 2
Use the diagram to fine the measure of the
indicated angle. Then classify the angle.
1. KHJ
2. GHK
3. GHJ
4. GHL
Example 3
Turn to page 28 of
your textbook. Use
your protractor to
measure the angles
shown for exercises
3-5.
Example 4
What is the measure
of DOZ?
D
G
25
O
40
Z
Example 4
You basically used the
Angle Addition
Postulate to get the
measure of the
angle, where
mDOG + mGOZ
= mDOZ.
D
G
25
O
40
Z
Angle Addition Postulate
If P is in the interior of RST, then
mRST = mRSP + mPST.
Example 5
Given that mLKN = 145°,
find mLKM and
mMKN.
M
L
2x+10
4x-3
K
N
Congruent Angles
• Two angles are congruent angles if
they have the same measure.
Add the appropriate
markings to your picture.
Patty Paper Activity
On a piece of patty
paper, use a
straightedge to
draw and label
acute angle ABC.
Patty Paper Activity
Fold the paper so
that BC coincides
with BA.
Patty Paper Activity
Unfold the paper and
draw point D on the
crease in the
interior of ABC.
What do you notice
about ABD and
DBC. BD is called
an angle bisector.
Angle Bisector
An angle bisector is a
ray that divides an
angle into two
congruent angles.
Example 6
In the diagram, YW
bisects XYZ, and
mXYW = 18°. Find
mXYZ.
X
W
Y
Z
Angle Pair Investigation
In this Investigation, you will be shown
examples and non-examples of various
angle pairs. Use the pictures to come up
with a definition of each angle pair.
Complementary Angles
Supplementary Angles
C Comes Before S…
m1  m2  90
m3  m4  90
m5  m6  180
m7  m8  180
Linear Pairs of Angles
Linear Pairs of Angles
• Two adjacent angles
form a linear pair if
their noncommon
sides are opposite
rays.
• The angles in a linear
pair are
supplementary.
Vertical Angles
Vertical Angles
• Two nonadjacent
angles are vertical
angles if their sides
form two pairs of
opposite rays.
• Vertical angles are
formed by two
intersecting lines.
Example 7
1. Given that 1 is a complement of 2 and
m1 = 68°, find m2.
2. Given that 3 is a complement of 4 and
m3 = 56°, find m4.
Example 8
Identify all of the linear pairs of angles and all
of the vertical angles in the figure.
Example 9
Two angles form a linear pair. The measure
of one angle is 5 times the measure of the
other angle. Find the measure of each
angle.