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Geometry Section 3-1 1112

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Parallel Lines and Transversals

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Geometry Section 3-1 1112

  1. 1. CHAPTER 3 Parallel and Perpendicular LinesTuesday, December 13, 2011
  2. 2. SECTION 3-1 Parallel Lines and TransversalsTuesday, December 13, 2011
  3. 3. ESSENTIAL QUESTIONS How do you identify the relationships between two lines or two planes? How do you name angle pairs formed by parallel lines and transversals?Tuesday, December 13, 2011
  4. 4. VOCABULARY 1. Parallel Lines: 2. Skew Lines: 3. Parallel Planes: 4. Transversal:Tuesday, December 13, 2011
  5. 5. VOCABULARY 1. Parallel Lines: Two or more lines in the same plane that do not intersect 2. Skew Lines: 3. Parallel Planes: 4. Transversal:Tuesday, December 13, 2011
  6. 6. VOCABULARY 1. Parallel Lines: Two or more lines in the same plane that do not intersect 2. Skew Lines: Two or more lines that are in different planes and do not intersect 3. Parallel Planes: 4. Transversal:Tuesday, December 13, 2011
  7. 7. VOCABULARY 1. Parallel Lines: Two or more lines in the same plane that do not intersect 2. Skew Lines: Two or more lines that are in different planes and do not intersect 3. Parallel Planes: Two or more planes that do not intersect 4. Transversal:Tuesday, December 13, 2011
  8. 8. VOCABULARY 1. Parallel Lines: Two or more lines in the same plane that do not intersect 2. Skew Lines: Two or more lines that are in different planes and do not intersect 3. Parallel Planes: Two or more planes that do not intersect 4. Transversal: A line that intersects two other coplanar lines at two different pointsTuesday, December 13, 2011
  9. 9. VOCABULARY 5. Interior Angles: 6. Exterior Angles: 7. Consecutive Interior Angles: 8. Alternate Interior Angles:Tuesday, December 13, 2011
  10. 10. VOCABULARY 5. Interior Angles: Angles that are formed in the region between two lines being intersected by a transversal 6. Exterior Angles: 7. Consecutive Interior Angles: 8. Alternate Interior Angles:Tuesday, December 13, 2011
  11. 11. VOCABULARY 5. Interior Angles: Angles that are formed in the region between two lines being intersected by a transversal 6. Exterior Angles: Angles that are formed in the region outside of the two lines being intersected by a transversal 7. Consecutive Interior Angles: 8. Alternate Interior Angles:Tuesday, December 13, 2011
  12. 12. VOCABULARY 5. Interior Angles: Angles that are formed in the region between two lines being intersected by a transversal 6. Exterior Angles: Angles that are formed in the region outside of the two lines being intersected by a transversal 7. Consecutive Interior Angles: Interior angles that are on the same side of the transversal, thus being “next” to each other 8. Alternate Interior Angles:Tuesday, December 13, 2011
  13. 13. VOCABULARY 5. Interior Angles: Angles that are formed in the region between two lines being intersected by a transversal 6. Exterior Angles: Angles that are formed in the region outside of the two lines being intersected by a transversal 7. Consecutive Interior Angles: Interior angles that are on the same side of the transversal, thus being “next” to each other 8. Alternate Interior Angles: Nonadjacent interior angles that are on opposite sides of the transversalTuesday, December 13, 2011
  14. 14. VOCABULARY 9. Alternate Exterior Angles: 10. Corresponding Angles:Tuesday, December 13, 2011
  15. 15. VOCABULARY 9. Alternate Exterior Angles: Nonadjacent exterior angles that are on opposite sides of the transversal 10. Corresponding Angles:Tuesday, December 13, 2011
  16. 16. VOCABULARY 9. Alternate Exterior Angles: Nonadjacent exterior angles that are on opposite sides of the transversal 10. Corresponding Angles: Angles that are on the same side of the transversal and on the same side of the lines being intersected by the transversal; these angles have the same positionTuesday, December 13, 2011
  17. 17. EXAMPLE 1 Identify each of the following using the box. a. All segments parallel to BC b. A segment that is skew to EH c. A plane that is parallel to plane ABGTuesday, December 13, 2011
  18. 18. EXAMPLE 1 Identify each of the following using the box. a. All segments parallel to BC FG, AD, EH b. A segment that is skew to EH c. A plane that is parallel to plane ABGTuesday, December 13, 2011
  19. 19. EXAMPLE 1 Identify each of the following using the box. a. All segments parallel to BC FG, AD, EH b. A segment that is skew to EH DC, CF, AB, or BG c. A plane that is parallel to plane ABGTuesday, December 13, 2011
  20. 20. EXAMPLE 1 Identify each of the following using the box. a. All segments parallel to BC FG, AD, EH b. A segment that is skew to EH DC, CF, AB, or BG c. A plane that is parallel to plane ABG Plane DECTuesday, December 13, 2011
  21. 21. EXAMPLE 2 Refer to the figure below. Classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. a. ∠2 and ∠6 b. ∠1 and ∠7Tuesday, December 13, 2011
  22. 22. EXAMPLE 2 Refer to the figure below. Classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. a. ∠2 and ∠6 b. ∠1 and ∠7 Corresponding AnglesTuesday, December 13, 2011
  23. 23. EXAMPLE 2 Refer to the figure below. Classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. a. ∠2 and ∠6 b. ∠1 and ∠7 Corresponding Angles Alternate Exterior AnglesTuesday, December 13, 2011
  24. 24. EXAMPLE 2 Refer to the figure below. Classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. c. ∠3 and ∠8 d. ∠3 and ∠5Tuesday, December 13, 2011
  25. 25. EXAMPLE 2 Refer to the figure below. Classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. c. ∠3 and ∠8 d. ∠3 and ∠5 Consecutive Interior AnglesTuesday, December 13, 2011
  26. 26. EXAMPLE 2 Refer to the figure below. Classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. c. ∠3 and ∠8 d. ∠3 and ∠5 Consecutive Interior Angles Alternate Interior AnglesTuesday, December 13, 2011
  27. 27. EXAMPLE 3 The driveways at a bus station are shown. Identify the transversal connecting each pair of angles in the figure. Then classify the relationship between each pair of angles. a. ∠1 and ∠2 b. ∠2 and ∠3Tuesday, December 13, 2011
  28. 28. EXAMPLE 3 The driveways at a bus station are shown. Identify the transversal connecting each pair of angles in the figure. Then classify the relationship between each pair of angles. a. ∠1 and ∠2 b. ∠2 and ∠3 v; CorrespondingTuesday, December 13, 2011
  29. 29. EXAMPLE 3 The driveways at a bus station are shown. Identify the transversal connecting each pair of angles in the figure. Then classify the relationship between each pair of angles. a. ∠1 and ∠2 b. ∠2 and ∠3 v; Corresponding v; Alternate InteriorTuesday, December 13, 2011
  30. 30. EXAMPLE 3 The driveways at a bus station are shown. Identify the transversal connecting each pair of angles in the figure. Then classify the relationship between each pair of angles. c. ∠4 and ∠5Tuesday, December 13, 2011
  31. 31. EXAMPLE 3 The driveways at a bus station are shown. Identify the transversal connecting each pair of angles in the figure. Then classify the relationship between each pair of angles. c. ∠4 and ∠5 y; Consecutive InteriorTuesday, December 13, 2011
  32. 32. CHECK YOUR UNDERSTANDING Check out the problems on p. 173 #1-12.Tuesday, December 13, 2011
  33. 33. PROBLEM SETTuesday, December 13, 2011
  34. 34. PROBLEM SET p. 174 #13-45 odd “It has long been an axiom of mine that the little things are infinitely the most important.” - Sir Arthur Conan DoyleTuesday, December 13, 2011

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