Prove Theorem 1. [Outline of proof (fill in all details): If C is any point of the segment , then A-C-B. If C ∈ ℓ or H2 then B ∈ ℓ (→←) or B-A-C (→←). (You need to prove that B-A-C holds in that case.) ∴ C ∈ H1 and segment ⊆ H1 except for A. Similarly, if D ∈ ray , and A-B-D, then it follows that D ∈ H1.]
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