1.2 Measurement of Segments and Angles

1.2 Measurement of Segments and AnglesKatie McDonaldAmelia OonMonica PacynaMeasuring Segments and AnglesSegment LengthUsually measured in inches, feet, yards, millimeters, centimeters, meters.To show the measure of a segment write MP instead of Angle MeasurementProtractor- an instrument marked in degrees used to measure anglesUsually measured in degrees ()

Examples -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

MP = 9

MPProtractorTo show measure of segment MP, we writeThe measure of this angle is 125

Classifying AnglesAcute Angles = angle measure > 0, but < 90

Obtuse Angles = angle measure > 90, but < 180

Right Angles = angle measure is 90

Straight Angles = angle measure is 180 (forms a straight line)ExamplesAcute angleObtuse angleRight angleStraight angleVideo!

Parts of Degree1 degree is equal to 60 minutes ( )1 minute is equal to 60 seconds ( )1 = 601 = 60Examples = + = 545

545 = + =

When changing to degrees and mins..multiply the fraction by 60.When changing to degrees..divide the mins by 60.Adding and Subtracting Since there are 60 minutes in a second, subtract 60 from 82 and add the one minute to 54When borrowing minutes, add 60 seconds instead of ten.302345 +151012 453357B) 122454 +103028 225482 225522

1268C) 241308 -051014 190254Congruent Angles and SegmentsCongruent Angles- angles that have the same measureCongruent Segments- segments that have the same lengthSymbol for congruent Tick marks indicate congruent segments and angles.

Tick MarksAdding AnglesIf two angles are congruent, set the angle measurements equal to each other and solve

If the two angles form a right angle, add the two and make them equal to 90

X+ 7PJ2x +10 P J

Find xX + 7 = 2x + 10-10 +7 = 2x x-3 = xG12G is a right angle1 = x+32 = x+5X + 3 + x + 5 = 902x + 8 = 902x = 82X = 41RestrictionsExample

Since K is an acute angle the angle has to be greater than 0 but less than 90. Therefore the restriction is 0< X < 90 XFind the restrictions on XK is an acute angle

KM2X+10M is an obtuse angleFind the restrictions on X

90 < 2x+10 < 18090-10< 2x< 180-1080< 2x < 170 240 < x < 85When finding restrictions on M, place the angle equation between 90 and 180, since it is an obtuse angle.

Clock ProblemsBecause an analog clock is shaped in a circle, it contains 360. If there are 12 hours represented on this circle, the space in between each number is 30 (360/12=30).Therefore, if the hands of the clock are on an even hour, count the spaces in between and multiply by thirty to calculate the measure of the angle that the hands form.For example, if it is 3:00, multiply the spaces between the twelve and the three by thirty to get the degree of the angle.3x30=90

12

Clock problems continued5. However, the hands on the clock will not always be exactly on an hour of the clock.6. In this case count the whole spaces between the min. hand and the hour hand, and do the same process as before. For example, if the time is 9:40, there is one whole space between the 9 and 8 which equals 307. To get the degrees between the 9 and hour hand, divide the min. by 60 and simplify. In our example, the equation would be . This fraction represents how far the hour hand is from the 9.8. Once a fraction is found, multiply it by 30 because there are 30 between two numbers. ( 30) = 209. If the hour hand makes the angle bigger when moved clockwise, add the two numbers. If the angle will be made smaller, subtract the number from 30 first, and then add. The result is the measure of the angle of the clocks hands.

13Example1212345678910112:45303030303030(5) = 150

( 30 ) = 22.5

150 + 22.5 = 172.5

Practice ProblemsAOProblem 1: -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

Find AOAO = 7Find the measure of the angle

The angles measure is 100Practices Problems Cont.Right Angle(90)B) Acute Angle 0< m < 90C) Straight Angle(180)

D) Obtuse Angle90 < m < 180 Match each angle with the correct name :m = measureEven More Practice Problems Change to Degrees and Minutes: = 3(1) + = 3 30

A)B)

7 36 =

= 7.6Here Come Some MoreAdd or Subtract:

28 30 12 +14 06 57

42 36 69 = 42 37 09B) 30 25 10 -07 05 32

23 19 382470

Almost DoneFind the congruent angles A)1)2)3)Find the congruent segments B)1)2)3)Keep Going1212345678910111:30Find the angles measure: 1:302 (30) = 60

= (30) = 15

60 + 15 = 75Almost there OM2xX+3O = MFind x

2x = x+3X = 312KK is a right angle1 = 2x +42 = 2x+2

Find x

2x+4+2x+2 = 904x+6 = 904x = 90-64x = 84X = 21

Last One!!!!Find the Restrictions on x

J is and obtuse anglexJ K is an acute angleK3x-3090 < 3x + 30 < 18090 30 < 3x < 180 3060 < 3x < 150 320