1.4 Measure and Classify Angles
You will name, measure and classify
angles.
Classifying Angles
• Acute angle: between 0 and 90
• Right angle: exactly 90 degrees
• Symbol:
• Obtuse Angle: between 90 and 180
• Straight angle: exactly 180 degrees
Angles
• Naming Angles
– Use 3 capital letters – Vertex in the middle
– Can use one capital letter if it is the vertex and it is
obvious which angle you are referring to
– Can use the number located inside the angle
• Angle Bisector
– Divides the angle into 2 congruent parts
Naming angles
• Name this angle three different ways
Naming angles
• Name this angle three different ways
Naming angles
• Name this angle four different ways
Name this angle in 4 ways
Congruent Angles
• Have the same angle measure
Congruent Angles
• Can be marked using the same number of
hash marks.
H
W
F
Q
Angle Addition Postulate
• Smaller angles can be added together to form
larger angles if they share a common vertex.
Given that the m<LKN=145⁰, find the
m<LKM and m<MKN
GUIDED PRACTICE
for Example 3
Find the indicated angle measures.
3.
Given that
<KLM is a straight angle, find x and m< NLM.
GUIDED PRACTICE
4.
for Example 3
Given that < EFG is a right angle, find x and m< HFG.
Homework
• Page 28 # 4 – 40 even
• Honors: also # 42, 44, 48, 49, 50
EXAMPLE 2
Measure and classify angles
Use the diagram to find the measure of the indicated angle. Then
classify the angle.
a.
KHJ
b.
GHK
c.
GHJ
d.
SOLUTION
A protractor has an inner and an outer
scale. When you measure an angle,
check to see which scale to use.
GHL
Angle Addition Postulate
• When two angles share a ray, a
Part+ Part = Whole or Little + Little = Big
• Very similar to segment addition Postulate
Congruent Angles
• Angles that have the same measure
• Angle measures are equal: m<A=m<B
– The measure of angle A is equal to the measure of
angle B
• Angle measures are congruent: <A
<B
– Angle A is congruent to angle B
• When talking about measures, use equal sign.
When talking about congruency, use
congruent sign
EXAMPLE 4
Identify congruent angles
The photograph shows some of the angles formed by the ropes
in a trapeze apparatus. Identify the congruent angles. If m<DEG = 157° ,what
is m<GKL?
GUIDED PRACTICE
for Example 4
Use the diagram shown.
5.
Identify all pairs of congruent angles in the diagram.
GUIDED PRACTICE
for Example 4
Use the diagram shown.
6.
In the diagram, m < PQR = 130 , m<QRS = 84, and m<TSR = 121 . Find the
other angle measures in the diagram.
Angle
• Formed by two rays that meet at an endpoint
• Rays are considered sides of an angle
• What is the vertex? What rays form the angle?
Vertex of an Angle
• Where the sides of an angle meet.
• When naming an angle, vertex goes in the
middle
Name the three angles in the diagram.
Angle bisector
A ray that divides an angle into two angles that are
congruent (equal)
In the diagram at the right, YW bisects < XYZ, and m< XYW = 18. Find
m< XYZ.
Protractor Postulate
• The rays of an angle can be matched one to
one with real numbers from 0 to 180
• The measure of an angle is equal to the
absolute value of the difference between the
real number of the rays (much like the
segment addition postulate)