Plane Geometry - Bruce E. Shapiro

SECTION 15. THE PLANE SEPARATION POSTULATE 77Figure 15.2: Definition of angle ∠CAB. The interior of the angle is theintersection of the two half-planes, and is shaded darker..BACDefinition 15.8 Let A, B, C be points such that the rays −→ −→ AB ≠ AC arenot opposite. The interior of ∠BAC isH B,←→ AC∩ H C,←→ AB,i.e., the intersection of the half plane H B determined by B and ←→ AC andthe half plane H C determined by C and AB (figure 15.2).Definition 15.9 Three points A, B, C are collinear if there exists a singleline l such that A, B, and C all lie on l. If no such line exists, then thepoints are non-collinear.Corollary 15.10 If A, B, and C are non-collinear, then the rays −→ AB and−→AC are neither opposite nor equal.Definition 15.11 Let A, B, and C be non-collinear points.triangle △ABC is the union of the three segments,Then the△ABC = AB ∪ BC ∪ CAThe points A, B, and C are called the vertices of the triangle, and thesegments AB, BC and CA are called the sides of the triangle.Revised: 18 Nov 2012 « CC BY-NC-ND 3.0.