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Advanced Geometry Parallel and Perpendicular Lines Lesson 1

Parallel Lines. Advanced Geometry Parallel and Perpendicular Lines Lesson 1. Lines (segments & rays, also) are either. parallel,. intersecting,. or skew. Skew Lines. do not intersect. are not coplanar. and. are skew. Planes can be parallel. OR. intersecting. Example :.

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Advanced Geometry Parallel and Perpendicular Lines Lesson 1

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  1. Parallel Lines Advanced Geometry Parallel and Perpendicular Lines Lesson 1

  2. Lines (segments & rays, also) are either parallel, intersecting, or skew.

  3. Skew Lines do not intersect are not coplanar and are skew.

  4. Planes can be parallel OR intersecting.

  5. Example: Name all segments that are parallel to . Figure from p. 143. Name all segments that intersect . Name all segments that are skew to . Name all planes that are parallel to plane DEF.

  6. Transversal Identify the pairs of lines to which each given line is a transversal. m landn; landp; nandp p landm; landn; mandn

  7. Whenever there are two lines and a transversal, eight angles are formed. t a b exterior angles – angles outside the two lines interior angles – angles between the two lines ∠3, ∠4, ∠5, ∠6 ∠1, ∠2, ∠7, ∠8

  8. ∠3 and ∠6 ∠4 and ∠5 AlternateInterior Angles AlternateInterior Angles AlternateInterior Angles AIA • both angles are interior t • different sides of the • transversal a Alternate Exterior Angles Alternate Exterior Angles Alternate Exterior Angles b AEA • both angles are exterior • different sides of the • transversal ∠1 and ∠8 ∠2 and ∠7

  9. ∠3 and ∠5 ∠4 and ∠6 ConsecutiveInterior Angles ConsecutiveInterior Angles ConsecutiveInterior Angles CIA • both angles are interior t • same side of the • transversal a Corresponding Angles b • one interior angle and • one exterior angle ∠1 and ∠5 ∠2 and ∠6 ∠3 and ∠7 ∠4 and ∠8 • same side of the • transversal

  10. Identify each pair of angles and AIA, AEA, CIA, corresponding angles, vertical angles, or a linear pair. ∠5 and ∠12 AEA corresponding angles ∠10 and ∠3 vertical angles ∠4 and ∠7 CIA ∠10 and ∠11 linear pair ∠2 and ∠12 AIA ∠3 and ∠14

  11. Name the transversal that forms each pair of angles. Then identify the pair of angles. a ∠8 and ∠6 corresponding angles b ∠10 and ∠14 AIA c ∠2 and ∠16 AEA b ∠10 and ∠11 CIA

  12. When the lines cut by a transversal are parallel, the four angle pairs have a special relationship. • AIA are congruent. Reminder: • Vertical angles • are ALWAYS • congruent. • AEA are congruent. • CIA are supplementary. • Linear pairs are • ALWAYS • supplementary. • Corresponding angles • are congruent.

  13. In the figure a || b and m∠4 = 51. Find the measures of all numbered angles. Justify each answer. a b

  14. Find the measure of each angle if m∠1 = 62 and m∠7 = 107.

  15. What is the measure of ∠RTV?

  16. If m∠2 = 4x + 7 and m∠3 = 5x – 13, find m∠3.

  17. If m∠5 = 2x – 10, m∠6 = 4(y – 25), and m∠7 = x + 15. find x and y.

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