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Geometry

Geometry. 3.3 Proving Lines Parallel. Postulate. ~. // Lines => corr. <‘s =. From yesterday : If two // lines are cut by a transversal, then corresponding angles are congruent. 2. 1. 4. 3. 5. 6. 8. 7. ~. <1 = <5. Postulate. Today , we learn its converse :

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Geometry

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  1. Geometry 3.3 Proving Lines Parallel

  2. Postulate ~ // Lines => corr. <‘s = From yesterday : If two // lines are cut by a transversal, then corresponding angles are congruent. 2 1 4 3 5 6 8 7 ~ <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. <‘s = => // Lines 2 1 4 3 5 6 8 7 ~ // If <1 = <5, then lines are

  4. Theorem ~ // Lines => alt int <‘s = From yesterday: If two // lines are cut by a transversal, then alternate interior angles are congruent. 2 1 4 3 5 6 8 7 ~ 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 <‘s = => // Lines 2 1 4 3 5 6 8 7 ~ // If <3 = <6, then lines are

  6. Theorem // Lines => SS Int <‘s supp From yesterday: If two // lines are cut by a transversal, then same side interior angles are supplementary. 2 1 4 3 5 6 8 7 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 <‘s supp => // Lines 2 1 4 3 5 6 8 7 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. t k l If kand l areboth to tthen the lines are//

  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 ?… A T W H Are WI and AN parallel? No, because <WIL and <ANI are not congruent 61 ≠ 62 22 23 61 62 N E L I Are HI and TN parallel? Yes, because <WIL and <ANI are congruent 61 + 23 = 84 62 + 22 = 84

  12. In Summary (the key ideas)………

  13. 5 Ways to Prove 2 Lines Parallel ~ • Show that a pair of Corr. <‘s are = • √ √ √ √ √ Alt. Int. <‘s are = • √√√√√ S-S Int. <‘s are supp • Show that 2 lines are to a 3rd line • √ √ √ √ √ to a 3rd 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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