Plane Geometry - Bruce E. Shapiro

80 SECTION 16. ANGLESFigure 16.1: The protractor postulate allows to associate a number between0 and 180 with every angle.BACIf µ(∠BAC) = 90 we call angle ∠BAC a right angle.Figure 16.2: Since point D is in the interior of angle ∠BAC, we say thatray −→−→ −→AD is between ray AB and AC. Furthermore, by the angle additionpostulate (axiom 16.2), γ = α + β, where α = µ(∠BAD), β = µ(∠DAC),and γ = µ(BAC).Definition 16.3 Two angles ∠BAC and ∠EDF are called congruent ifµ(∠BAC) = µ(∠EDF ), and we write ∠BAC ∼ = ∠EDFTheorem 16.4 Let l be a line, A ∈ l, B ∉ l, and A ∗ C ∗ B. Then B andC are on the same side of l (figure 16.3.)Proof. Let m = ←→ AB. Lines m and l are not parallel since they share pointA, and since B ∉ l then m ≠ l. Hence by theorem 13.9 they interesect at« CC BY-NC-ND 3.0. Revised: 18 Nov 2012