Plane Geometry - Bruce E. Shapiro

SECTION 29. TRANSVERSALS 135Corollary 29.5 If m ⊥ l and n ⊥ l, then either m = n or m ‖ n.Proof. (Exercise)Corollary 29.6 If one pair of corresponding angles is congruent, so is theother pair.Proof. (Exercise)Corollary 29.7 (Corresponding Angles Theorem) If l and m are linescut by a transversal to t in such a way that two corresponding angles arecongruent, then l ‖ m.Proof. (Exercise)Figure 29.4: The corresponding angles theorem: lines a and b are parallelbecause they are cut by a transversal that has congruent correspondingangles.Corollary 29.8 If l and m are lines cut by a transversal t in such a way thattwo non-alternating interior angles on the same side of t are supplements,then l ‖ m.Proof. (Exercise)Revised: 18 Nov 2012 « CC BY-NC-ND 3.0.