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Geometry 3.3 Proving Lines Parallel. Postulate From yesterday : If two // lines are cut by a transversal, then corresponding angles are congruent. //

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Presentation on theme: "Geometry 3.3 Proving Lines Parallel. Postulate From yesterday : If two // lines are cut by a transversal, then corresponding angles are congruent. //"— Presentation transcript:

1 Geometry 3.3 Proving Lines Parallel

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

3 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 // ~

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

5 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 ~ //

6 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

7 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 //

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

9 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

10 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...

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

12 In Summary (the key ideas)………

13 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 ~ ~

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

15 Homework pg. 87 # 1-27 odd


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