You will learn to measure, draw, and classify angles.
1) Degrees
2) Protractor
3) Right Angle
4) Acute Angle
In geometry, angles are measured in units called _______.degrees
In geometry, angles are measured in units called _______.degrees
The symbol for degree is °.
Q
P
R 75°
In the figure to the right, the angle is 75 degrees.
In notation, there is no degree symbol with 75 because the measure of an angle is a real number with no unit of measure.
Postulate 3-1 Angles Measure Postulate
For every angle, there is a unique positive number
between __ and ____ called the degree measure of the angle.
B
A
C n°
Postulate 3-1 Angles Measure Postulate
For every angle, there is a unique positive number
between __ and ____ called the degree measure of the angle. B A C n° 0
Postulate 3-1 Angles Measure Postulate
For every angle, there is a unique positive number
between __ and ____ called the degree measure of the angle. B A C n° 0 180
Postulate 3-1 Angles Measure Postulate
For every angle, there is a unique positive number
between __ and ____ called the degree measure of the angle. B A C n° 0 180
m ABC = n and 0 < n < 180
J H
G
S
Q R
m SRQ =
Find the measurement of:
m SRJ =
m SRG =
m QRG =
m GRJ =
J H
G
S
Q R
m SRQ =
Find the measurement of:
m SRJ =
m SRG =
m QRG =
m GRJ =
180 45 150
70
180 – 150 = 30
150 – 45 = 105
Use a protractor to draw an angle having a measure of 135. 1) Draw AB
Use a protractor to draw an angle having a measure of 135. 1) Draw AB
2) Place the center point of the protractor on A. Align the mark labeled 0 with the ray.
Use a protractor to draw an angle having a measure of 135. 1) Draw AB
2) Place the center point of the protractor on A. Align the mark labeled 0 with the ray.
3) Locate and draw point C at the mark labeled 135. Draw AC.
Use a protractor to draw an angle having a measure of 135. 1) Draw AB
2) Place the center point of the protractor on A. Align the mark labeled 0 with the ray.
3) Locate and draw point C at the mark labeled 135. Draw AC.
C
Once the measure of an angle is known, the angle can be classified as one of three types of angles. These types are defined in relation to a right angle.
Once the measure of an angle is known, the angle can be classified as one of three types of angles. These types are defined in relation to a right angle.
Types of Angles
Once the measure of an angle is known, the angle can be classified as one of three types of angles. These types are defined in relation to a right angle.
Types of Angles
obtuse angle
90 < m A < 180
Once the measure of an angle is known, the angle can be classified as one of three types of angles. These types are defined in relation to a right angle.
Types of Angles
A
obtuse angle
90 < m A < 180
Once the measure of an angle is known, the angle can be classified as one of three types of angles. These types are defined in relation to a right angle.
Types of Angles
A
right angle
m A = 90 obtuse angle
90 < m A < 180
Once the measure of an angle is known, the angle can be classified as one of three types of angles. These types are defined in relation to a right angle.
Types of Angles
A
right angle
m A = 90
A
obtuse angle
90 < m A < 180
Once the measure of an angle is known, the angle can be classified as one of three types of angles. These types are defined in relation to a right angle.
Types of Angles
A
right angle
m A = 90
acute angle
0 < m A < 90
A
obtuse angle
90 < m A < 180
Classify each angle as acute, obtuse, or right.
110°
90° 40°
50°
Classify each angle as acute, obtuse, or right.
110°
90° 40°
50°
130° 75°
Obtuse
Obtuse
Acute
Acute Acute
5x - 7 B
The measure of B is 138. Solve for x.
5x - 7 B
The measure of B is 138. Solve for x.
B = 5x – 7 and B = 138 Given: (What do you know?)
5x - 7 B
The measure of B is 138. Solve for x.
B = 5x – 7 and B = 138 Given: (What do you know?)
5x – 7 = 138 5x = 145 x = 29
5x - 7 B
The measure of B is 138. Solve for x.
B = 5x – 7 and B = 138 Given: (What do you know?)
5x – 7 = 138 5x = 145
x = 29 5(29) -7 = ?
145 -7 = ? 138 = 138
9y + 4 H
The measure of H is 67. Solve for y.
9y + 4 H
The measure of H is 67. Solve for y.
H = 9y + 4 and H = 67 Given: (What do you know?)
9y + 4 H
The measure of H is 67. Solve for y.
H = 9y + 4 and H = 67 Given: (What do you know?)
9y + 4 = 67 9y = 63 y = 7
9y + 4 H
The measure of H is 67. Solve for y.
H = 9y + 4 and H = 67 Given: (What do you know?)
9y + 4 = 67 9y = 63
y = 7 9(7) + 4 = ?
63 + 4 = ? 67 = 67
• If you have the sides 3 and 8, what is the
possible range for the third side?
|Side 1 – Side 2| = Lower Bound
|Side 1 + Side 2| = Upper Bound
|3-8| = 5 and |3+8| = 11 so the range is 5<x<11 where x is the third side. This means x can be any number between (but not Including) 5 and 11.
• The longest side of a triangle is opposite
the ______ angle.
• The smallest angle is opposite the _____
side.
E A C B D
