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Parallel Lines and Transversals

Parallel Lines and Transversals

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Parallel Lines and Transversals

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  1. Parallel Lines and Transversals Chapter 3-1

  2. Identify the relationships between two lines or two planes. • Name angles formed by a pair of lines and a transversal. • parallel lines • consecutive interior angles • alternate exterior angles • alternate interior angles • corresponding angles • parallel planes • skew lines • transversal Preparation for Standard 7.0Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. (Key) Lesson 3-1 Ideas/Vocabulary

  3. Parallel Lines // • Two lines are // if they are coplanar and do not intersect. Triangles are used to indicate // lines

  4. Skew Lines • Lines that do not intersect but are not coplanar are called skew lines.

  5. Parallel Planes • Two planes that do not intersect.

  6. B C D A G F H E Based on looks, find a line: • // to AB and containing D •  to AB and containing D • Skew to AB and containing D • Name the plane(s) that contain D and appear to be // to plane ABE 1. DC 2. AD 4. DCH or DGH or DCG 3. DH

  7. Identify Relationships A. Name all planes that are parallel to plane AEF. Answer: plane BHG Lesson 3-1 Example 1a

  8. __ B. Name all segments that intersect AF. __ __ __ __ Answer:EF, GF, DA, and BA Identify Relationships Lesson 3-1 Example 1b

  9. __ C. Name all segments that are skew to AD. __ __ __ __ __ Answer:FG, GB, EH,EC, and CH Identify Relationships Lesson 3-1 Example 1c

  10. A • B • C • D A. Name a plane that is parallel to plane RST. plane WTZ plane SYZ plane WXY plane QRX Lesson 3-1 CYP 1a

  11. B. Name a segment that intersects YZ. A. B. C. D. XY WX QW RS Lesson 3-1 CYP 1b

  12. C. Name a segment that is parallel to RX. A. B. C. D. ZW TZ QR ST Lesson 3-1 CYP 1c

  13. D. Name a segment that is skew to TZ. __ __ __ ___ ___ RX ST XW QW • A • B • C • D Lesson 3-1 CYP 1d

  14. t 1 2 3 4 6 5 7 8 Transversal • A line that intersects two or more coplanar lines at different points. t is a transversal

  15. Identify Transversals A. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line v is a transversal. Answer: If the lines are extended, line v intersects lines u, w, x, and z. Lesson 3-1 Example 2a

  16. Identify Transversals B. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line y is a transversal. Answer: lines u, w, x,z Lesson 3-1 Example 2b

  17. Identify Transversals C. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line u is a transversal. Answer: lines v, x, y,z Lesson 3-1 Example 2c

  18. A. HIKING A group of nature trails is shown. Identify the sets of lines to which line a is a transversal. • A • B • C • D lines c, f lines c, d, e lines c, d, f lines c, d, e, f Lesson 3-1 CYP 2a

  19. B. HIKING A group of nature trails is shown. Identify the sets of lines to which line b is a transversal. • A • B • C • D no lines lines c, f lines c, d, e, f lines a, c, d, e, f Lesson 3-1 CYP 2b

  20. C. HIKING A group of nature trails is shown. Identify the sets of lines to which line c is a transversal. • A • B • C • D lines a, b lines a, b, d, e, f lines a, d, f lines a, b, e Lesson 3-1 CYP 2c

  21. D. HIKING A group of nature trails is shown. Identify the sets of lines to which line d is a transversal. • A • B • C • D lines e, f lines a, b, f lines a, b, c, e, f lines a, b, c Lesson 3-1 CYP 2d

  22. t 1 2 3 4 6 5 7 8 Corresponding Angles 1 and 5 are corresponding s • Two angles that occupy corresponding positions. 2 and 6 are corresponding s 3 and 7 are corresponding s 4 and 8 are corresponding s

  23. t 1 2 3 4 6 5 7 8 Alternate Interior Angles • Two angles that lie between the two lines on opposite sides of the transversal. 3 and 6 are Alt. Int. s 4 and 5 are Alt. Int. s

  24. t 1 2 3 4 6 5 7 8 Alternate Exterior Angles • Two angles that lie outside the two lines on opposite sides of the transversal. 1 and 8 are Alt. Ext. s 2 and 7 are Alt. Ext. s

  25. t 1 2 3 4 6 5 7 8 Consecutive Interior Angles • Two angles that lie between the two lines on the same side of the transversal. 3 and 5 are Consecutive Int. s 4 and 6 are Consecutive Int. s Sometimes called Same Side Interior Angles

  26. A. Identify 7 and 3 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Identify Angle Relationships Answer: corresponding Lesson 3-1 Example 3a

  27. B. Identify 8 and 2 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Identify Angle Relationships Answer: alternate exterior Lesson 3-1 Example 3b

  28. C. Identify 4 and 11 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Identify Angle Relationships Answer: corresponding Lesson 3-1 Example 3c

  29. D. Identify 7 and 1 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Identify Angle Relationships Answer: alternate exterior Lesson 3-1 Example 3d

  30. E. Identify 3 and 9 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Identify Angle Relationships Answer: alternate interior Lesson 3-1 Example 3e

  31. F. Identify 7 and 10 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Identify Angle Relationships Answer: consecutive interior Lesson 3-1 Example 3f

  32. A. Identify 4 and 5. • A • B • C • D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3a

  33. B. Identify 7 and 9. • A • B • C • D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3b

  34. C. Identify 4 and 7. • A • B • C • D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3c

  35. D. Identify 2 and 11. • A • B • C • D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3d

  36. E. Identify 3 and 5. • A • B • C • D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3e

  37. F. Identify 6 and 9. • A • B • C • D alternate interior alternate exterior corresponding consecutive interior Lesson 3-1 CYP 3e

  38. 9 12 10 11 2 3 1 4 7 6 8 5 Practice

  39. Homework pg. 144 12-19, 24-35, 41-44