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Geometry 3.3 Proving Lines Parallel

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Postulate From yesterday : If two // lines are cut by a transversal, then corresponding angles are congruent. // Lines => corr. <‘s = ~ <1 = <5 ~

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Postulate Today, we learn its converse : If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. corr. // Lines ~ If <1 = <5, then lines are // ~

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Theorem From yesterday: If two // lines are cut by a transversal, then alternate interior angles are congruent. // Lines => alt int <‘s = ~ Example: <3 = <6 ~

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Theorem Today, we learn its converse : If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. alt int // Lines ~ If <3 = <6, then lines are ~ //

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Theorem From yesterday: If two // lines are cut by a transversal, then same side interior angles are supplementary. // Lines => SS Int <‘s supp Example: <4 is supp to <6

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Theorem Today, we learn its converse : If two lines are cut by a transversal and same side interior angles are supplementary, then the lines are parallel. SS Int // Lines If <4 is supp to <6, then the lines are //

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Theorem From yesterday: If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.

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Theorem Today, we learn its converse: In a plane two lines perpendicular to the same line are parallel. If k and l are both to t then the lines are // k l t

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3 More Quick Theorems Theorem:Through a point outside a line, there is exactly one line parallel to the given line. Theorem:Through a point outside a line, there is exactly one line perpendicular to the given line. Theorem:Two lines parallel to a third line are parallel to each other...

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Which segments are parallel ?… WH AT LI NE Are WI and AN parallel? No, because

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In Summary (the key ideas)………

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5 Ways to Prove 2 Lines Parallel 1. Show that a pair of Corr. <‘s are = 2. √ √ √ √ √ Alt. Int. <‘s are = 3. √ √ √ √ √ S-S Int. <‘s are supp 4. Show that 2 lines are to a 3 rd line 5. √ √ √ √ √ to a 3 rd line ~ ~

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Turn to pg. 87 Let’s do #19 and # 28 from your homework together

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Homework pg. 87 # 1-27 odd

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