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 AB 1234 AB |2-3|or|3-2| = |-1|= |1|= 1 The length of AB = 1 cm cm

Measuring angles: Unit of measure: Degrees Radians Grads 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°.

P A R m<PAR = 90  m<A = 90  Angle measurement m<1 = 135  1

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  = 87  30’ 90  = 89  59’60”

Find m<CBD A B C D m<ABD = 90  m<ABC = 74  21’10” 90  - 74  21’ 10” 15  38’50” 89  59’ 60” - 74  21’ 10”

Congruent angles and segments Symbol: = = < have the same measure = have the same length <A = <B A 60 B 60

Congruency Tick marks show congruency A C B X ZY Name congruent angles and segments.

Example A B C 1 2 m<ABC = 90  m<1 = (3x+4)  m<2 = (x+6)  Find both angles! 3x x + 6 = 90 4x + 10 = 90 4x = 80 x = 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 360 º 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 67.5 º. 7.5 º 2 intervals for a total of 60 º. 30 º