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Bell Ringer #

Bell Ringer #. 3-2 Proving Lines Parallel. Postulate 3-2 Converse of the Corresponding Angles Postulate. If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel. 1. m ‖ n. m. 2. n. Theorems.

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Bell Ringer #

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  1. Bell Ringer #

  2. 3-2 Proving Lines Parallel

  3. Postulate 3-2 Converse of the Corresponding Angles Postulate • If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel. 1 m ‖ n m 2 n

  4. Theorems • 3-3 Converse of the Alternate Interior Angles Thm • If two lines and a transversal form alternate interior angles that are congruent, then the lines are parallel. 3-4 Converse of the Same-Side Interior Angles Thm. • If two lines and a transversal form same-side interior angles that are supplementary, then the lines are parallel

  5. If ∠1 ≅ ∠2, then m ‖ n • If ∠2 and ∠4 are supplementary, then m‖ n m 4 1 2 n

  6. Flow Proof • Arrows show the logical connections between the statements. • Proving theorem 3-3 • Given: ∠1 ≅ ∠2 • Prove: m‖n 3 m 2 1 n

  7. Theorems • Theorem 3-5 • If two lines are parallel to the same line, then they are parallel to each other. • Theorem 3-6 • In a plane, if two lines are perpendicular to the same line, then they are parallel to each other a t b c m n

  8. Examples • 1. which lines must be parallel if ∠1 ≅ ∠2? Justify using a theorem or postulate. 3 E C 4 D 1 K 2

  9. 3. Use algebra to find the value of x. 40° (2x + 6)°

  10. 4. Find the value of x. (7x – 8)° 62°

  11. Ticket Out The Door

  12. Practice • Pg 125-126 • 1-3, 18 -20, and 27 - 30

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