If , then must ray  pass through an interior point of  ∠ABC? The affirmative answer to thi...

If , then must ray  pass through an interior point of  ∠ABC? The affirmative answer to this is the essence of the converse statement of Axiom A-2: If m∠ABD + m∠DBC = m∠ABC, then ray  passes through an interior point of

∠ABC. Fill in the details of the following indicated steps in its proof: Locate points K, L, and M on rays respectively. Case 1: When K, L, and M are collinear and lie on line ℓ (not passing through B), then either K-L-M, K-M-L, or L-K-M. Use Axiom A-2, first part, to gain a contradiction if either K-M-L or L-K-M. Case 2: When K,L, and M are noncollinear, the cases are (a) B lies in the interior of all three angles of the triangle KLM (show you get a contradiction here by using the Linear Pair Axiom and by extending ray  backward to form ray , intersecting  by the Crossbar Theorem), or (b) B lies on the opposite side of one of the lines  as the respective points M, K, or L. Show this case reverts back to Case 1, already proven.