Plane Geometry - Bruce E. Shapiro

SECTION 22. NEUTRAL GEOMETRY 109Neutral Geometry Axiom 5 (Protractor Postulate) (Axiom 16.2)For every angle ∠BAC there is a real number µ(∠BAC) called the measureof ∠BAC such that(a) 0 ≤ µ(∠BAC) < 180(b) µ(∠BAC) = 0 ⇐⇒ −→ −→ AB = BC.(c) 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.−→−→ −→(d) Angle Addition Postulate: If AD is between rays AB and ACthenµ(∠BAD) + µ(∠DAC) = µ(∠BAC) (22.1)Neutral Geometry Axiom 6 (Side Angle Side (SAS) Postulate)(Axiom 21.2) If △ABC and △DEF are two triangles such that AB ∼ = DE,∠ABC ∼ = ∠DEF , and BC ∼ = EF then △ABC ∼ = △DEF .Revised: 18 Nov 2012 « CC BY-NC-ND 3.0.