Plane Geometry - Bruce E. Shapiro

Section 30Triangles in NeutralGeometryDefinition 30.1 The angle sum of △ABC is defined asσ(△ABC) =µ(∠CAB) + µ(∠ABC) + µ(∠BCA)Figure 30.1: Theorem 30.2 says that β + γ < 180.Theorem 30.2 The sum of the measure of any two angles in a triangle isless than 180: For any triangle △ABC,µ(∠CAB) + µ(∠ABC) < 180Proof. Let D ∈ ←→ AB such that A ∗ B ∗ D (see figure 30.1).By the linear pair theorem (thm. 18.4), α + β = 180.137