Proving Lines Parallel What You'll Learn You will learn to identify conditions that produce parallel lines. Reminder: In Chapter 1, we discussed “if-then” statements (pg. 24). Within those statements, we identified the “__________” and the “_________”. hypothesis conclusion I said then that in mathematics, we only use the term “if and only if” if the converse of the statement is true.

Proving Lines Parallel Postulate 4 – 1 (pg. 156): IF ___________________________________, THEN ________________________________________. two parallel lines are cut by a transversal two parallel lines are cut by a transversal each pair of corresponding angles is congruent each pair of corresponding angles is congruent The postulates used in §4 - 4 are the converse of postulates that you already know. COOL, HUH?

Proving Lines Parallel Postulate 4-2 In a plane, if two lines are cut by a transversal so that a pair of corresponding angles is congruent, then the lines are _______. parallel 1 2 a b If <1 ≅ <2, then _____ a || b

Proving Lines Parallel Theorem 4-5 In a plane, if two lines are cut by a transversal so that a pair of alternate interior angles is congruent, then the two lines are _______. parallel 1 2 a b If <1 ≅ <2, then _____ a || b

Proving Lines Parallel Theorem 4-6 In a plane, if two lines are cut by a transversal so that a pair of alternate exterior angles is congruent, then the two lines are _______. parallel 1 2 a b If <1 ≅ <2, then _____ a || b

Proving Lines Parallel Theorem 4-7 In a plane, if two lines are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the two lines are _______. parallel 1 2 a b If <1 + <2 = 180, then _____ a || b

Proving Lines Parallel Theorem 4-8 In a plane, if two lines are cut by a transversal so that a pair of consecutive interior angles is supplementary, then the two lines are _______. parallel If a t and b t, then _____ a b t a || b

Proving Lines Parallel We now have five ways to prove that two lines are parallel. Concept Summary Show that a pair of corresponding angles is congruent. Show that a pair of alternate interior angles is congruent. Show that a pair of alternate exterior angles is congruent. Show that a pair of consecutive interior angles is supplementary. Show that two lines in a plane are perpendicular to a third line.

Proving Lines Parallel Identify any parallel segments. Explain your reasoning. G A Y D R 90°

Proving Lines Parallel Find the value for x so BE || TS. E B S T (6x - 26)° (2x + 10)° (5x + 2)°

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