6 1. Trisecting Angles Figure 1.1.7 Figure 1.1.8 5. Give another proof of Proposition 1.1.3 as follows. Construct the points A and B as in the original proof, but then use Proposition 1.1.1 to bisect ∠AQB. Show that the bisecting line is perpendicular to . 1.2. Two facts from geometry In this short section we recall a pair of facts obtained in elementary geometry that will be frequently used. No proofs are given. 1.2.1. Proposition. If AB and CD are two parallel lines and they are cut by a third line EF that meets the first two at the points P and Q, respectively (see Figure 1.2.1), then ∠APF = ∠CQF , ∠BPE = ∠DQE, and so on. Figure 1.2.1

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