Transcript 1 4 Angles

1.4: Measure and Classify Angles
Objectives:
1. To define, classify, draw,
name, and measure
angles
2. To use the Protractor
and Angle Addition
Postulates
3. To construct congruent
angles and angle
bisectors with compass
and straightedge
Assignment:
• P. 28-32: 2, 4, 6, 1226 even, 30, 40, 42,
48-50, 64, 65
• Challenge Problems
You will be able to define,
classify, draw, name, and
measure angles
Objective 1
Angle
An angle consists of
two different rays
(sides) that share a
common endpoint
(vertex).
Angle 𝐴𝐵𝐶, ∠𝐴𝐵𝐶, or ∠𝐵
Exercise 1
Which numbered angle is the same as
∠𝐴𝐵𝐶? Explain.
Exercise 2
Explain why you
can’t call ∠𝐹𝐷𝐺
simply ∠𝐷.
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?
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.
0° < 𝑚∠𝑃 < 180°
Measured with a protractor
Classifying Angles
Surely you are familiar with all of my angular
friends by now.
The measure of this
angle is written as
𝑚∠𝐴𝐵𝐶 = 34°
How To Use a Protractor
Exercise 3
Complete your
Protractor Practice
worksheet.
1. Write your answer in
the form 𝑚∠𝐴𝐵𝐶 =
2. Draw your angles on
the back and label
them something!
Exercise 4
What is 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.
Exercise 5
Given that 𝑚∠𝐿𝐾𝑁 = 145°,
find 𝑚∠𝐿𝐾𝑀 and
𝑚∠𝑀𝐾𝑁.
M
L
2x+10
4x-3
K
N
Objective 3
You will be able to construct congruent
angles and angle bisectors with
compass and straightedge
Congruent Angles
Two angles are congruent angles if they
have the same measure.
Congruent Angles
Draw angle A on your paper. How could you
copy that angle to another part of your
paper using only a
compass and a
straightedge?
Congruent Angles
1. Draw angle A.
Congruent Angles
2. Draw a ray with endpoint A’.
Congruent Angles
3. Put point of compass on A and draw an
arc that intersects both sides of the angle.
Label these points
B and C.
Congruent Angles
4. Put point of compass on A’ and use the
compass setting from Step 3 to draw a
similar arc on the ray.
Label point B’ where
the arc intersects
the ray.
Congruent Angles
5. Put point of compass on B and pencil on
C. Make a small arc.
Congruent Angles
6. Put point of compass on B’ and use the
compass setting from Step 5 to draw an
arc that intersects the
arc from Step 4.
Label the
new point
C’.
Congruent Angles
7. Draw ray A’C’.
Angle Bisector
An angle
bisector is a ray
that divides an
angle into two
congruent angles.
Bisect an Angle
1. Draw an acute angle and label the vertex
A.
Bisect an Angle
2. Using vertex A as the center, draw an arc
intersecting both sides of your angle. Label the
intersections B and C.
Bisect an Angle
3. Using the same compass setting, draw two
intersecting arcs in the interior of your angle,
one centered at B, the other centered at C.
Bisect an Angle
4. Label the intersection D.
Bisect an Angle
5. Draw a ray from vertex A through point D.
Exercise 6
In the diagram,𝑌𝑊
bisects ∠𝑋𝑌𝑍, and
𝑚∠𝑋𝑌𝑊 = 18°.
Find 𝑚∠𝑋𝑌𝑍.
X
W
Y
Z
Exercise 7
In the diagram, 𝑂𝐸 bisects ∠𝐿𝑂𝑁. Find the value of
𝑥 and the measure of each angle.
1.4: Measure and Classify Angles
Objectives:
1. To define, classify, draw,
name, and measure
angles
2. To use the Protractor
and Angle Addition
Postulates
3. To construct congruent
angles and angle
bisectors with compass
and straightedge
Assignment:
• P. 28-32: 2, 4, 6, 1226 even, 30, 40, 42,
48-50, 64, 65
• Challenge Problems