Download Section 1.2: Measurement of Segments and Angles - Math2014-2015

Name _________________________________________________________________Date _______________________ Geometry A
Section 1.2: Measurement of Segments and Angles
Objective: To classify angles by size, name the parts of a degree, and recognize congruent angles and
segments.
Do Now: Name the following as many ways as possible.
1.
K
m
L
2.
T
3.
C
A
F
B
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Measuring Segments
Some of the units that are commonly used to measure segments are inches, feet, yards, millimeters,
centimeters, and meters. To indicate the measure of AB , we write AB.
Example: If AB is 5 cm long, we write AB  5 cm .
Classifying Angles by Size
Acute Angle- An angle whose measure is greater than __________ and less than ___________.
Right Angle- An angle whose measure is _________.
Obtuse Angle- An angle whose measure is greater than ________ and less than __________.
Straight Angle- An angle whose measure is __________.
Parts of a Degree
As you know, each hour of the day is divided into 60 minutes and each minute is divided into 60
seconds. Similarly, each degree (  ) of an angle is divided into 60 minutes ( ’ ) and each minute of an
angle is divided into 60 seconds ( ’’ ).
60  1
60  1
(60 minutes equals 1 degree)
(60 seconds equals 1 minute)
Convert to degrees and minutes.
1. 87½° = _________° _________’
2. 60.4° = _________° _________’
3. 90° = _________° _________’
4. 180  = _________° _________’
Convert to degrees, minutes and seconds.
5. 90° = _______° _______’ _______’’
6. 12 92 ° = _______° _______’ _______’’
Convert to degrees only.
7. 42° 12’ = ___________ 
9. Given: ABC is a right angle.
ABD  67  21 37
8. 60° 45’= ___________ 
10. Subtract.
6115
 40  26
Find: DBC
A
D
B
C
Congruent Angles and Segments
Congruent angles are angles that have the same measure. Congruent segments are segments that
have the same length. The symbol for congruence is __________. Identical tick marks are used to indicate
congruent angles and segments.
Z
K
Y
S
G
H
W
T
R
X
Name the congruent parts. _____________________________________________________________________________________
Sample Problems
1. Given: ÐDEF @ ÐFEG , ÐDEF = (6x + 6)o, ÐFEG = (2x + 30)o
Find: mÐDEG (the measure of ÐDEG )
D
K
F
G
E
M
J
H
2. Given: ÐDEG = 80o, ÐDEF = 50o, ÐHJM =120o, ÐHJK = 90o
Draw a conclusion about FEG and KJM .
D
K
F
G
E
H
M
J
3. Given: ABC is a right angle, 1  (3x  4)  , 2  ( x  6) 
Find m1
A
1
B
2
C
4. C is acute.
a) What are the restrictions on mC ?
C
(2x+14)
b) What are the restrictions on x?
5. Find the angle formed by the hands of a clock at each time. Always look for the angle less than 180.
a) 2:00
b) 4:15
c) 5:50
Homework: Section 1.2 (page 14) # 1, 2, 4, 5, 6, 8, 9, 11, 13, 16, 17, 20, 21