Plane Geometry - Bruce E. Shapiro

Section 29TransversalsDefinition 29.1 Suppose that lines m = ←→ AC and n = ←→ DF are distinct.Suppose that a third line l = ←→ AB intersects m at a point B and line n at apoint E ≠ B. Then l is a transversal to lines m and n (see figure 29.1),and we say that m and n are cut by transversal l.Definition 29.2 Consider the transversal as illustrated in figure 29.1. Theangles α, β, γ, and δ are called interior angles. The pairs {α, δ} and{β, γ} are called alternate interior angle pairs.Figure 29.1: Lines ←→ AC and ←→ DF are cut by transversal ←→ BE. Angles α andδ form an alternating interior angle pair, as do angles γ and β.Definition 29.3 Suppose that lines ←→ AC and ←→ DF are cut by a transversal←→BE as illustrated in figure 29.2. Then angles α and β as shown are calledcorresponding angles. If µ(α) = µ(β) then α and β are called congruentcorresponding angles.133