1.2 Measurement of Segments and Angles

Measuring Segments

Match item being measured with proper unit.

U.S.: Inches, feet, yards, miles etc.Metric: km, cm, m, mm

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

Measuring angles:

Unit of measure:DegreesRadiansGrads

Tool: protractor

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°.

PA R

m<PAR = 90m<A = 90

Angle measurement

m<1 = 1351

Classify angles by size

Acute: 0<x<90

Right: 90 Obtuse: 90<x<180

Straight: 180

Parts of a degree:

1 Degree = 60’ (minutes)1 Minute = 60” (seconds)So, 87 = 8730’

12

90 = 8959’60”

Find m<CBD

A

B

C

D

m<ABD = 90

m<ABC = 7421’10”

90

- 7421’ 10” 1538’50”

8959’ 60”- 7421’ 10”

Congruent angles and segments

Symbol: == < have the same measure= have the same length

<A = <B

A 60 B 60

Congruency

Tick marks show congruencyA

CB

X

Z Y

Name congruent angles and segments.

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°

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