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Aim:

Aim:. k. 1. 2. 3. 4. 6. How do we prove lines are parallel?. 5. l. 7. 8. Do Now:. 1) Name 4 pairs of corresponding angles. 2) Name 2 pairs of alternate interior angles. 3) Name 2 pairs of alternate exterior angles.

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Aim:

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  1. Aim: k 1 2 3 4 6 How do we prove lines are parallel? 5 l 7 8 Do Now: 1) Name 4 pairs of corresponding angles. 2) Name 2 pairs of alternate interior angles. 3) Name 2 pairs of alternate exterior angles. 4) If lines l and k are extended and they never intersect, what can we say about l and k ? l || k 5) If lines l and k are extended and they do intersect, what can we say about l and k ? l is not || k Geometry Lesson:

  2. Def: Parallel lines have no points in common or have all points in common. B F D A E C l k Line m is “transverse” to lines l and k. m Def. Parallel: Def: Transversal Def: A transversal is a line that intersects two other lines in two different points. Geometry Lesson: Proving Lines are Parallel

  3. 4 8 3 7 2 6 1 5 Transversals/ angle pairs: Geometry Lesson: Proving Lines are Parallel

  4. 7 5 4 6 3 2 1 1 2 3 4 Ex: Transversals/ angle pairs State the type of each angle pair: alt. interior corresponding alt. interior alt. exterior alt. interior alt. interior Geometry Lesson: Proving Lines are Parallel

  5. l 4 8 Theorem #11: 3 7 2 Two lines cut by a transversal are parallel if a pair of corresponding angles are congruent. 6 1 5 Theorem #12: Two lines cut by a transversal are parallel if a pair of alternate interior angles are congruent. Theorem #13: Two lines cut by a transversal are parallel if a pair of interior angles on the same side of the transversal are supplementary. Theorem #14: Two lines perpendicular to the same line are parallel. Proving lines parallel m k Geometry Lesson: Proving Lines are Parallel

  6. 1) E ( D C ( A B A B C D 2) 3) E 4) 48 D 132 C ( C D ) A B A B Ex: Proving lines parallel Or Geometry Lesson: Proving Lines are Parallel

  7. D C A B ?  Ex: Proving lines parallel Geometry Lesson: Proving Lines are Parallel

  8. C Given: 1 3 D B 2 Prove: A Ex Proving lines parallel: Given Given Def. angle bisector Transitive Postulate Geometry Lesson: Proving Lines are Parallel

  9. R L D A S S Q M 3) Given: E F Prove: P D 1 2 3 4 M B R C Proving lines parallel: 1) Given: Prove: 2) Given: Prove: Geometry Lesson: Proving Lines are Parallel

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