3. Prove Lemma 1.1.6: For any three distinct lines L1, L2, and I plane, if L1||L2 and L2||L3, then L1||L3. Hint: You m

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3 Prove Lemma 1 1 6 For Any Three Distinct Lines L1 L2 And I Plane If L1 L2 And L2 L3 Then L1 L3 Hint You M 1 (4.59 KiB) Viewed 73 times

3 Prove Lemma 1 1 6 For Any Three Distinct Lines L1 L2 And I Plane If L1 L2 And L2 L3 Then L1 L3 Hint You M 2 (39.34 KiB) Viewed 73 times

3. Prove Lemma 1.1.6: For any three distinct lines L1, L2, and I
plane, if L1||L2 and L2||L3, then L1||L3. Hint: You may follow the outline of a proof by contradiction below, in which case you must provide a valid justification for the steps (1), (2) and (3). Outline of a proof by contradiction. Suppose Lemma 1.1.6 is not true. Then (a) There exist three distinct lines L1, L2, and L3 such that L1||L2. L2||L3 and L1 L3 because [Your justification of the step (1) goes here] (b) For such lines L1, L2, and L3, there exists a point P such that L and L3 intersect at P because .... [Your justification of the step (2) goes here] (c) Construct a statement that contradicts Parallel Postulate. Your justification of the step (3) goes here as well. This contradicts Parallel Postulate. Therefore, Lemma 1.1.6 must be true.