Transcript Interactive Chalkboard

1.4 Angle Measures
Objectives:
How to label, measure, and classify angles
 Identifying and using congruent angles
 Creating and utilizing an angle bisector

Rays
A ray
 is part of a line which has one endpoint
and extends infinitely in one direction.
 named stating the endpoint first and then
any other point on the ray.

Labeling Rays

We could label this
ray as AB, AC, or
AD but not CA.
D
C
B
A
More about Rays

If you choose a point on a line, that point
determines exactly two rays called
opposite rays.
P
Q
QP and QR are
opposite rays.
R
Angles and Their Parts

An angle is formed by two noncollinear
rays that have a common endpoint.
– the rays are called sides
– common endpoint is the vertex.
B
Side AB
Side AC
A
Vertex A
C
Labeling Angles

We label angles any of the following ways:
BAC,
CAB,
A, or
1
B
1
A
C
More about Angles

An angle divides a plane into three distinct
parts. Points A, B, and C lie on the angle.
Points D and E line in the interior of the
angle. Points F and G lie in the exterior
of the angle.
B
D
F
1
E
G
C
A
Example 1a:
Name all angles that have B as a vertex.
Answer: 5, 6, 7, and ABG
Example 1b:
Name the sides of 5.
Answer:
and
or
are the sides of 5.
Example 1c:
Write another name for 6.
Answer: EBD, FBD, DBF, and DBE
are other names for 6.
Your Turn:
a. Name all angles that have X as a vertex.
Answer: 1, 2, 3, and RXB
or RXN
b. Name the sides of 3.
Answer:
c. Write another name for 3.
Answer: AXB, AXN, NXA, BXA
Measuring Angles

To measure an angle we use a
protractor.
– Place the center of the protractor on the
vertex and one side of the angle on either
side of the 0° line of the protractor.
– The protractor will have two scales running
from 0° to 180° in opposite directions.
– Read the measure of the angle by viewing the
alignment of the other side of the angle with
the proper scale.
Classifying Angles

There are four types of angles.
Acute angles measure < 90°.
Right angles measure 90°.
Obtuse angles measure > 90° but < 180°.
Straight angles measure 180°.
Example 2a:
Measure TYV and classify it as
right, acute, or obtuse.
TYV is marked with
a right angle symbol,
so measuring is not
necessary.
Answer:
is a right angle.
Example 2b:
Measure WYT and classify it as
right, acute, or obtuse.
Use a protractor to find
that
.
Answer:
>
is an obtuse angle.
Example 2c:
Measure TYU and classify it as
right, acute, or obtuse.
Use a protractor to find
that m
.
Answer:
is an acute angle.
Your Turn:
Measure each angle named and classify
it as right, acute, or obtuse.
a. CZD
Answer: 150, obtuse
b. CZE
Answer: 90, right
c. DZX
Answer: 30, acute
Congruent Angles

Just as segments that have equal measures are
congruent, angles that have the same
measures are congruent. To label angles
congruent we use tic marks just like we used for
segments.
A
BAC 
C
X
YXZ
B
Y
Z
More about Congruent Angles

A ray that divides an angle into two
congruent angles is called an angle
bisector. If AD bisects BAC then
BAD is congruent to CAD.
B
D
A
C
Example 3:
INTERIOR DESIGN Wall stickers of standard shapes
are often used to provide a stimulating environment
for a young child’s room. A five-pointed star sticker
is shown with vertices labeled. Find mGBH and
mHCI if GBH HCI, mGBH 2x + 5, and
mHCI 3x – 10.
Example 3:
Given
Definition of congruent angles
Substitution
Add 10 to each side.
Subtract 2x from each side.
Example 3:
Use the value of x to find the measure of one angle.
Given
or 35
Since
Answer: Both
Simplify.
.
measure 35.
Your Turn:
SIGNS A railroad crossing sign forms congruent
angles. In the figure, WVX ZVY. If mWVX 7a + 13
and mZVY 10a – 20, find the actual measurements of
WVX and ZVY.
Answer:
Assignment:

Geometry:
Pg. 34 – 35, #12 - 37

Pre-AP Geometry:
Pg. 34 – 35, #12 – 39, 45 - 48