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Section 1-4: Measuring Angles
SPI 32A: Identify properties of plane figures from information in a
diagram
Objective:
• Classify and find the measure of angles
Angle
Formed by two rays with the same endpoint.
Rays
Vertex
(endpoint)
Naming Angles
1
Name the Rays of the angle:
BA
What is the vertex of the angle?
BC
Vertex is B
Different ways to name the angle:
• Name by vertex: B
• Name by 3 points (vertex in middle):  ABC or 
CBA
• Name by a number:  1
Geometry is used to construct roofs. Use the diagram below to
answer the following questions.
G
1 2
H
I
F
What is the vertex of the large angle? The vertex is G
Name the Rays of the angle:
GF , GH ,GI
Name all the angles in the diagram using both letters & numbers.
• 1
• 2
• FGI
• IGF
• IGH • FGH
• HGI • HGF
Measuring Angles and the Protractor Postulate
Postulate 1-7 Protractor Postulate
For every angle, there corresponds a number between 0 and 180º. This
number is called the measure of the angle and is written in degrees.
Four Different Classifications of Angles
Right Angle
Straight Angle
Acute Angle
Obtuse Angle
Using a Protractor to Measure Angles
1.
2.
3.
4.
Place the vertex at zero on the protractor
Align one ray with the bottom edge of the protractor
Read measurement (in degrees) on protractor
Caution:
Pay attention to the numbers
Ensure answer makes sense
What type of angle is represented in the diagram?
Angle Addition Postulate
Postulate 1-8
Angle Addition Postulate
AXB and BXD form linear pairs
and are adjacent angles
G
If the mDEG = 145º , find the mGEF.
145º + _____
35 = 180
Name the adjacent angles? Are they a linear pair?
D
E
F
Suppose that m
1 = 42 and m
ABC = 88. Find m
2.
What postulate do you use to solve the problem?
Use the Angle Addition Postulate to solve.
m
1+m
2=m
ABC Angle Addition Postulate.
42 + m
2 = 88
Substitute 42 for m
m
2 = 46
Subtract 42 from each side.
1 and 88 for m
ABC.
Congruency of Angles and Triangles
According to the diagram above, the following congruency
statements are true:
mA = mD, therefore AD
mB = mE, therefore BE
mC = mF, therefore CF
Explain which angles and line segments are congruent by looking
at the figures.
Write congruency statements based on the statement
∆DEF  ∆GHI.