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Geometry

Geometry. 3.1 Lines and Transversals. Parallel Lines // Lines. Coplanar lines that do not intersect j // k. k. j. Skew Lines. Noncoplanar lines that do not intersect line g is skew to line h g and h are skew lines. h. g. // and Skew Lines.

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Geometry

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  1. Geometry 3.1 Lines and Transversals

  2. Parallel Lines // Lines • Coplanar lines that do not intersect j // k k j

  3. Skew Lines • Noncoplanar lines that do not intersect line g is skew to line h g and h are skew lines h g

  4. // and Skew Lines • What are some // lines in the diagram? • What are some skew lines in the diagram? B F E A G C D H

  5. Segments and rays… …contained in // lines are also parallel. . B . D . C . A AB // CD AB // CD

  6. Are segments QP and RS parallel? • They do not intersect! • But they are parts of lines PQ and RS, which are not parallel.. • Thus, the answer is no! P Q R S

  7. // Planes…do not intersect • What are some parallel planes in the diagram? • Example: Plane ABCD // Plane EFGH B F E A G C D H

  8. A line and a plane are // if they do not intersect! • Examples? • Example: Plane ABCD // EF B F E A G C D H

  9. Theorem • If two parallel planes are cut by a third plane, then the lines of intersection are parallel. j k j // k

  10. Transversal • A line that intersects two or more coplanar lines in different points. t t is a transversal The lines do not need to be parallel to have a transversal !

  11. Interior Angles and Exterior Angles • Exterior angles 1, 2, 7, and 8. • Interior angles 3, 4, 5, and 6. t 1 2 4 3 5 6 7 8 The lines do not need to be parallel for this to be true!

  12. Alternate Interior Angles(Alt. Int <‘s) • Two nonadjacent interior angles on opposite sides of the transversal. • What are the two pairs of Alt. Int. <‘s? t 1 2 4 3 5 6 7 8 <4 and <5 <3 and <6 The lines do not need to be parallel for this to be true!

  13. Same Side Interior Angles(S.S. Int <‘s) • Two interior angles on the same side of the transversal. • What are the two pairs of S.S. Int. <‘s? t 1 2 4 3 5 6 7 8 <4 and <6 <3 and <5 The lines do not need to be parallel for this to be true!

  14. Corresponding Angles(Corr. <‘s) • Two angles in corresponding positions relative to the two lines. • What are the four pairs of Corr. <‘s? t 1 2 4 3 5 6 7 8 <2 and <6 <1 and <5 <3 and <7 <4 and <8 The lines do not need to be parallel for this to be true!

  15. Finding a transversal • Trace each < identified. • The line you touch twice is the transversal. • Name the two lines and the transversal between angles…It helps to draw an isolated picture B D Angles 1 and 5 2 Transversal AE Angles 2 and 6 1 F E 7 Transversal BC 3 A 4 5 8 Angles 4 and 7 Transversal EF 6 C

  16. Sometimes, Always, or Never? • When there is a transversal of 2 lines, the 3 lines are _________ coplanar. • Answer: Always • 2 Lines that are not coplanar __________ intersect. • Answer: Never • 2 Planes // to the same line are _________ // to each other. • Answer: Sometimes

  17. Review Sheet

  18. Please open your books to page 76 #4, 6, 12, 18, 24, 26, 34, 38 4) Alt. Int <‘s 6) Corr. <‘s 8) Lines PS, QR, and transversal SQ 12) Corr. <‘s 18) Corr. <‘s are congruent 24) GH, ED, KJ 26) CDJI and GHIJKL 34) Sometimes 38) Sometimes

  19. HW • P. 76 – 77, #1-41 odd, skip 19 and 21 • Self Test P. 65 Odds • Vocab Quiz tomorrow, Chapter 2 Test Friday • Ch. Review Today

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