Plane Geometry - Bruce E. Shapiro

Section 16AnglesDefinition 16.1 Ray −→−→ −→AD is between rays AB and AC if D is in theinterior of angle ∠BAC (figure 16.2), and we write 1−→AB ∗ −→ −→ AD ∗ ACAxiom 16.2 (Protractor Postulate) For every angle ∠BAC there is areal number µ(∠BAC) called the measure of ∠BAC such that1. 0 ≤ µ(∠BAC) < 1802. µ(∠BAC) = 0 ⇐⇒ −→ −→ AB = AC3. Angle Construction Postulate: For every number r ∈ (0, 180)and for each half plane H bounded by ←→ AB there exists a unique ray−→AE such that E ∈ H and µ(∠BAE) = r.4. Angle Addition Postulate If −→−→ −→AD is between rays AB and AC thenµ(∠BAD) + µ(∠DAC) = µ(∠BAC)When it is clear from the context that we are referring to the measure ofthe angle rather than the angle itself we will sometimes drop the µ andinstead of writing, say µ(∠BAC) = 45 we will just say ∠BAC = 45.If µ(∠BAC) < 90 we call angle ∠BAC an acute angle.If µ(∠BAC) > 90 we call angle ∠BAC an obtuse angle.1 The asterisk (∗) notation for rays is not used in the text but we will find it a convenientshorthand.79