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Name _________________________________________________________________Date _______________________ Geometry A Section 1.2: Measurement of Segments and Angles Objective: To classify angles by size, name the parts of a degree, and recognize congruent angles and segments. Do Now: Name the following as many ways as possible. 1. K m L 2. T 3. C A F B ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Measuring Segments Some of the units that are commonly used to measure segments are inches, feet, yards, millimeters, centimeters, and meters. To indicate the measure of AB , we write AB. Example: If AB is 5 cm long, we write AB 5 cm . Classifying Angles by Size Acute Angle- An angle whose measure is greater than __________ and less than ___________. Right Angle- An angle whose measure is _________. Obtuse Angle- An angle whose measure is greater than ________ and less than __________. Straight Angle- An angle whose measure is __________. Parts of a Degree As you know, each hour of the day is divided into 60 minutes and each minute is divided into 60 seconds. Similarly, each degree ( ) of an angle is divided into 60 minutes ( ’ ) and each minute of an angle is divided into 60 seconds ( ’’ ). 60 1 60 1 (60 minutes equals 1 degree) (60 seconds equals 1 minute) Convert to degrees and minutes. 1. 87½° = _________° _________’ 2. 60.4° = _________° _________’ 3. 90° = _________° _________’ 4. 180 = _________° _________’ Convert to degrees, minutes and seconds. 5. 90° = _______° _______’ _______’’ 6. 12 92 ° = _______° _______’ _______’’ Convert to degrees only. 7. 42° 12’ = ___________ 9. Given: ABC is a right angle. ABD 67 21 37 8. 60° 45’= ___________ 10. Subtract. 6115 40 26 Find: DBC A D B C Congruent Angles and Segments Congruent angles are angles that have the same measure. Congruent segments are segments that have the same length. The symbol for congruence is __________. Identical tick marks are used to indicate congruent angles and segments. Z K Y S G H W T R X Name the congruent parts. _____________________________________________________________________________________ Sample Problems 1. Given: ÐDEF @ ÐFEG , ÐDEF = (6x + 6)o, ÐFEG = (2x + 30)o Find: mÐDEG (the measure of ÐDEG ) D K F G E M J H 2. Given: ÐDEG = 80o, ÐDEF = 50o, ÐHJM =120o, ÐHJK = 90o Draw a conclusion about FEG and KJM . D K F G E H M J 3. Given: ABC is a right angle, 1 (3x 4) , 2 ( x 6) Find m1 A 1 B 2 C 4. C is acute. a) What are the restrictions on mC ? C (2x+14) b) What are the restrictions on x? 5. Find the angle formed by the hands of a clock at each time. Always look for the angle less than 180. a) 2:00 b) 4:15 c) 5:50 Homework: Section 1.2 (page 14) # 1, 2, 4, 5, 6, 8, 9, 11, 13, 16, 17, 20, 21