Proof Geometry 4-2: Angle Postulates

Measuring Angles Angles are measured in degrees If there are 50° in ABC, we write mABC=50 Note we do not include the degree sign because it is implied by mABC

The Angle Measurement Postulate To every angle, , there corresponds a real number between 0 and 180. This number is called the measure of , written m .

The Angle Construction Postulate   H H mPAB=r

Angle Addition Postulate C If D is in the interior of BAC, then mBAC = mBAD + mDAC (part + part = whole)

Angle Addition Postulate with Subtraction property of equality Angle addition postulate: mBAC = mBAD + mDAC Sub. Prop. Of eq. - mDAC - mDAC mBAC - mDAC = mBAD

Linear Pair Definition: If and are opposite rays, and is another ray from the shared vertex A, then BAC and  CAD form a linear pair C B A D

Supplementary angles Definition: The sum of the measures of two angles is 180, then the angles are called supplementary

The Supplement Postulate If two angles form a linear pair, then they are supplementary C B A D

Homework p. 87-91: # 1-5, 8, 13-16, 21. For 16 write a linear equation involving the measure of the angle x.