1. Measurement MA418 – Spring 2010 McAllister

2. Ruler Postulate (p. 41) Every line can be made into an exact copy of the real number line using a 1-1 correspondence. Line segments can be associated with a number that we call its measure. –Line segments with the same measure are said to be congruent. Lines and rays are infinite and can not be measured.

3. Protractor Postulate (p. 42) If we place one ray of an angle at 0 degrees on a protractor and the vertex at the midpoint of the bottom edge of the protractor, then there is a 1-1 correspondence between all other rays that can serve as the second (terminal) side of the angle and the real numbers between 0 and 180 inclusive, as indicated by a protractor.

4. Two types of angle measurement systems Degrees – minutes – seconds (fractional form) and decimal degrees. –There are 60 minutes in 1 degree and 60 seconds in 1 minute – so 32° 15’ 30” (32 degrees, 15 minutes, 30 seconds) is like [32 + 15/60 + 30/(60x60)] degrees. –We can convert this to decimal degrees by dividing out the fractions: so 32° 15’ 30” ≈ [32 + 0.25 + 0.0083] degrees

5. Now let’s go from decimal degrees to fractional form Suppose we have 241.32 degrees. If we want this in degrees – minutes seconds, we convert the decimal fraction part of the number back into fraction form. 0.32 x 60 = 19.2, so the 19 becomes the minutes and we convert the.2 to seconds. 0.2 x 60 = 12 So 241.32° = 241° 19’ 12”

6. Let’s practice on these examples Convert from d-m-s to decimal form –45° 16’ 43” –137° 47” Convert from decimal form to d-m-s –96.125° –101.027°