2. Katie McDonald Amelia Oon Monica Pacyna

3. I. Segment Length A. Usually measured in inches, feet, yards, millimeters, centimeters, meters. B. To show the measure of a segment write MP instead of II. Angle Measurement A. Protractor- an instrument marked in degrees used to measure angles B. Usually measured in degrees (°)

4.  -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 MP = 9 M P Protractor To show measure of segment MP, we write… The measure of this angle is 125°

5.  Acute 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)

6. Acute angle Obtuse angle Right angle Straight angle

8. 1 degree is equal to 60 minutes ( ‘ ) 1 minute is equal to 60 seconds ( “ ) 1° = 60‘ 1’ = 60” Examples ° = + = 5°45’ 5°45’ = + = ° When changing to degrees and mins..multiply the fraction by 60. When changing to degrees..divide the mins by 60.

9. Since there are 60 minutes in a second, subtract 60 from 82 and add the one minute to 54 When borrowing minutes, add 60 seconds instead of ten. A)30°23’45’’ +15°10’12’’ 45°33’57’’ B) 12°24’54’’ +10°30’28’’ 22°54’82’’ 22°55’22’ 12’68” C) 24°13’08’’ -05°10’14’’ 19°02’54’’

10.  Congruent Angles- angles that have the same measure  Congruent Segments- segments that have the same length  Symbol for congruent –  Tick marks indicate congruent segments and angles. Tick Marks

11.  If 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+ 7 P J 2x +10 P J Find x X + 7 = 2x + 10 -10 +7 = 2x – x -3 = x G 1 2 G is a right angle 1 = x+3 2 = x+5 X + 3 + x + 5 = 90 2x + 8 = 90 2x = 82 X = 41

12.  Example 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° X Find the restrictions on X K is an acute angle K M 2X+10 M is an obtuse angle Find the restrictions on X 90° < 2x+10 < 180° 90-10< 2x< 180-10 80< 2x < 170 2 40 < x < 85 When finding restrictions on M, place the angle equation between 90° and 180°, since it is an obtuse angle.

13. 1. Because 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). 2. 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. 3. 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. 4. 3x30=90°

14. 5. 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 30° 7. 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) = 20° 9. 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 clock’s hands.

15. 30° 30°(5) = 150 ( 30 ) = 22.5 150 + 22.5 = 172.5°

16. A O Problem 1: -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 Find AO AO = 7 Find the measure of the angle The angle’s measure is 100°

17. A)Right Angle(90°) B ) Acute Angle 0°< m < 90° C ) Straight Angle(180°) D) Obtuse Angle 90° < m < 180° Match each angle with the correct name : m = measure

18.  Change to Degrees and Minutes: = 3(1) + = 3° 30’ A) B) 7° 36’ = = 7.6°

19.  Add or Subtract: A)28° 30’ 12’’ +14° 06’ 57’’ 42° 36’ 69’’ = 42° 37’ 09’’ B) 30° 25’ 10’’ -07° 05’ 32’’ 23° 19’ 38’’ 24’70”

20.  Find the congruent angles A) 1) 2) 3) Find the congruent segments B) 1) 2) 3)

21. Find the angles measure: 1:30 2 (30) = 60 = (30) = 15 60 + 15 = 75°

22. O M 2x X+3 O = M Find x 2x = x+3 X = 3 1 2 K K is a right angle 1 = 2x +4 2 = 2x+2 Find x 2x+4+2x+2 = 90 4x+6 = 90 4x = 90-6 4x = 84 X = 21

23.  Find the Restrictions on x J is and obtuse angle x J K is an acute angle K 3x-30 90° < 3x + 30 < 180° 90 – 30 < 3x < 180 – 30 60 < 3x < 150 3 20 <x < 50 90° < x < 180°

24.  "Measuring an Angle with a Protractor." kwizNetLearningSystem. Web. 17 Jan 2010..  Rhoda, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge. Evanston, Illinois: McDougal Littell/Houghton Mifflin, 2007. Print.