Download 1-4

1-4 Angle Measure
What is a protractor and why is it used?
You measured line segments.
• Measure and classify angles.
• Identify and use congruent angles and the
bisector of an angle.
Vocabulary
Ray part of a line. It has one endpoint and
extends infinitely in one direction.
D
O
G
To name a ray, start with the endpoint
followed by another point on the ray.
P
O
N
M
Vocabulary
Opposite rays are two rays sharing a
common end point.
Vocabulary
Angle is formed by two rays (that are not
collinear) with a common endpoint or vertex.
The two rays are the sides of the angle.
An angle is named by
using three different
letters. The vertex letter
is always in the middle.
When there are no other
angles around, the angle
may be named by the
letter at the vertex.
R
side
S
vertex
side
T
Vocabulary
An angle divides a plane into three
distinctive parts:
On the angle
In the interior of the angle
R
In the exterior of the angle side
S
vertex
side
T
W
X
Name the angle in four ways.
A
B
1
C
Measuring Angles
Angles have different sizes and are usually
measured in degrees.
Angles measure between 0° and 180°.
The measure of an angle is written mXYZ  80
The size of of an angle is not the same thing as
the angle itself.
Protractor
Using a Protractor to measure
Using a protractor to measure
More Vocabulary
Measure and Classify Angles
A. Measure TYV and classify it as right, acute, or
obtuse.
Answer: mTYV = 90, so TYV is a right angle.
Measure and Classify Angles
Answer: 180 > mWYT > 90,
so WYT is an obtuse angle.
Measure and Classify Angles
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
Step 1 Solve for x.
GBH  HCI
mGBH = mHCI
2x + 5 = 3x – 10
2x + 15 = 3x
15 = x
Given
Definition of congruent angles
Substitution
Add 10 to each side.
Subtract 2x from each side.
Example 3
Step 2 Use the value of x to find the measure of
either angle.
.
Answer: mGBH = 35, mHCI = 35
Construction: Copy an Angle
1. Draw an angle to copy.
2. Draw a ray for your construction area.
3. Put the sharp tip of your compass on the
vertex (point) of the angle to copy.
4. Draw an arc crossing both sides of the angle
5. Without changing the size of your compass,
put the point on the end point of your ray.
Make an arc.
6. Go back to the angle and put each point of
your compass on the spot that the arc
crosses the sides of the angle.
Copy an Angle
7. Without moving the size of the compass,
put the pointed tip on the spot where the arc
crosses the ray. Make a mark that crosses the
arc.
8. Connect the endpoint and the curved “X” to
finish your constructed angle.
You have constructed congruent angles!!
Construction: Bisect an Angle
1. Draw an angle on your paper.
2. Put the point of your compass on the vertex and
draw a large arc.
3. Without moving the compass, put the point on the
bottom side where the arc crossed the side. Make
a mark in the interior of the angle.
4. Turn the compass and put the point on the other
side where the arc crosses the side. Make a mark
in the interior of the angle crossing the other mark.
5. Draw a ray connecting the vertex and the “X”.
You have bisected an angle!!
Assignment 1-4
p. 41, 13-17 odd,
21-25 odd, 33,
35, 47, 49