1. By Katherine Roberts & Allison Stroyan -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 Measurement of Segments and Angles Measure Segments Measure Angles Classify Angles By Size Naming Parts of a Degree Recognize Congruent Angles and Segments

2. A segment can be measured using a ruler or meter stick, using either metric units or inches, feet, etc. A segment can also be measured if it is placed on a number line. This is done by counting the units between the two endpoints of the segment. The length of AB is 6 units, because it starts on 1 and ends on 7 (7-1=6). 1 2 3 4 5 6 7 A B

3. If AL is 9 units long and it starts at -3 where does it end? -3 -2 -1 0 ? A L If JM starts at -7 and ends at 5, how long is JM? -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 J M Answers: AL ends at 6 and JM is 12 units long.

4. Angles are measured in degrees (°), and degrees are commonly measured by a protractor. Definition of measure : “the amount of turning you would do if you were at the vertex, looking along one side, and then turned to look along the other side” (Rhoad 9). Therefore, the protractor is placed at the angle’s vertex, aligned with one of the angle’s rays, and the measure is taken like so: In this course, angles will be > 0, and < 180. The Angle shown is 120˚

5. Answer: 145˚

6. Acute AngleRight AngleObtuse AngleStraight Angle

7. 46˚ 115˚ 92˚ B A C D E F G 59˚ Answers: Acute: D,G. Right: A,F. Obtuse: C,E. Straight: B

8. Each degree is divided into 60 minutes (‘), and each minute is divided into 60 seconds (“). Therefore: 56¾° = 56°45 ’ In order to get the 45, one must multiply the fraction in the degree by sixty to get its minute equivalent. 11.7° = 11°42’ The same rule applies with decimals in converting degrees to minutes. 78° = 77°60’ (since 60’ =1°) 143° = 142°59’60” (since 60” = 1’ and 60’ = 1°)

9. 154˚ 37’ 30” 98˚ 48’ 13˚ 40’ 102˚ 10’ 1.137° 40’ = 2.68° 16’ = 3.175° 7’ 30” = 4.47° 22’ 30” = 5.13  ° = 6.102  ° = 7.98  ° = 8.154  ° = 137  ° 2 3 2 3 1 6 4 5 5 8 68  ° 4 15 175  ° 1 8 47  ° 3 8

10. 100° AB 1 2 3 4 5 6 7 8 9 10 A SK R If two segments have the same length, they are congruent ( ≅ ). AS ≅ KR

11. If a segment is 9 units long and another segment starts at -4 and ends at 5 are the segments congruent? No (60  20 = 3, 3 * 11 = 33, 33 ≠ 39) Yes (4 + 5 = 9, 9 9) If an angle is 78° 39’ and another angle is 78 are they congruent?

12. Rhoad, Richard, George Milkauskas, Roberts Whipple, Geometry for Enjoyment and Challenge. Evanston, Illinois: McDougal Littell & Company, 1991. 9-17. Print.