1.2 Measurement of Segments and Angles. Measuring Segments Match item being measured with proper...
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1.2 Measurement of Segments and Angles
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Measuring Segments
Match item being measured with proper unit.
U.S.: Inches, feet, yards, miles etc.Metric: km, cm, m, mm
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Distance: absolute value
m AB1 2 3 4
A B
|2-3| or |3-2|= |-1| = |1|= 1 = 1
The length of AB = 1 cm
cm
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Measuring angles:
Unit of measure:DegreesRadiansGrads
Tool: protractor
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Angle measurement
Angle measurement is the opening from one ray to the next ray.We usually use the inside measurement, 180° or less.
A full turn is a circle and measures 360°.
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PA R
m<PAR = 90m<A = 90
Angle measurement
m<1 = 1351
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Classify angles by size
Acute: 0<x<90
Right: 90 Obtuse: 90<x<180
Straight: 180
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Parts of a degree:
1 Degree = 60’ (minutes)1 Minute = 60” (seconds)So, 87 = 8730’
12
90 = 8959’60”
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Find m<CBD
A
B
C
D
m<ABD = 90
m<ABC = 7421’10”
90
- 7421’ 10” 1538’50”
8959’ 60”- 7421’ 10”
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Congruent angles and segments
Symbol: == < have the same measure= have the same length
<A = <B
A 60 B 60
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Congruency
Tick marks show congruencyA
CB
X
Z Y
Name congruent angles and segments.
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ExampleAB
C
12
m<ABC = 90
m<1 = (3x+4)m<2 = (x+6)
Find both angles!
3x + 4 + x + 6 = 904x + 10 = 904x = 80x = 20
m<1 = 64°m<2 = 26°
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Find the measure of the angle formed by the hands of a clock at
5:15.• The hour hand is on 5 only when the minute hand is on 12.
• How far will the hour hand be away from 5 when it is 5:15?
• It will be ¼ of the way between the 5 and the 6.
• How many degrees is that?• There are 360º in the clock. Every 5
minutes has how many degrees?• ¼ of 30 is • How many “5 minute” intervals do
you need to add to that?• The angle measure of 5:15 is 67.5º.
7.5º
2 intervals for a total of 60º.
30º