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Geometry 3.1: Relationships Between Lines

Geometry 3.1: Relationships Between Lines. B. C. A. D. F. G. E. H. Parallel lines: Coplanar lines that never intersect (they will go in the same direction). Symbols:. Ex: AB || DC. B. C. A. D. F. G. E. H. Perpendicular Lines: Intersect at a right angle. Symbols:.

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Geometry 3.1: Relationships Between Lines

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  1. Geometry 3.1: Relationships Between Lines

  2. B C A D F G E H Parallel lines: Coplanar lines that never intersect (they will go in the same direction). Symbols: Ex: AB || DC

  3. B C A D F G E H Perpendicular Lines: Intersect at a right angle. Symbols: Ex: AB AE

  4. B C A D F G E H Skew Lines: Noncoplanar lines that do not intersect (they will go in different directions) Ex: AB and DH

  5. CAREFUL! c a b Remember to visualize in 3D! Line c intersects line b, but lines a and c are skew.

  6. B C A D F G E H Parallel Planes: planes in the same direction that will not intersect Ex: Plane ABC and Plane FEH

  7. N M E H T X O R S G A 1) Name all segments parallel to QX. NE, MH, TO, SG, RA Q

  8. N M E H T X O R S G A 1) Name all segments parallel to QX. NE, MH, TO, SG, RA 2) Name all planes that intersect plane MHE. Planes MNQ MHT HEX NEX Q

  9. N M E H T X O R S G A 1) Name all segments parallel to QX. NE, MH, TO, SG, RA 2) Name all planes that intersect plane MHE. Planes MNQ MHT HEX NEX 3) Name all segments parallel to QR. XA MT HO Q

  10. N M E H T X O R S G A 1) Name all segments parallel to QX. NE, MH, TO, SG, RA 2) Name all planes that intersect plane MHE. Planes MNQ MHT HEX NEX 3) Name all segments parallel to QR. XA, MT, HO Q 4) Name all segments skew to AG. TO, MH, NE, XQ TS, MT, NQ, QR

  11. Transversal • A line that intersects 2 or more coplanar lines at different points. • Ex: • Nonexample: Does not intersect the two lines at two different points!

  12. Corresponding Angles • 2 angles in corresponding positions (same side of transversal, same respective side of lines)

  13. Alternate Interior Angles • 2 angles between the two lines on opposite sides of transversal

  14. Same-Side Interior Angles(aka consecutive interior) • 2 angles between the two lines on the same side of transversal

  15. Alternate Exterior Angles • 2 angles outside the two lines on opposite sides of transversal

  16. Determining what type of angle pair • Locate angles & determine which line is transversal (this is always the line containing one side of both angles) • On which side of the transversal are the angles located? • Same side? Corresponding or SS Int (between the two lines) • Opposite side? • Alternate interior (angles are between the two lines) or • Alternate Exterior (angles are outside the two lines)

  17. 5) <1 and <8 Alternate exterior 6) <1 and <14 Alternate exterior 7) <4 and <12 corresponding Determine relationship between the two angles. 4 1 2 3 5 8 6 7 12 11 9 10 16 13 14 15

  18. 8) <6 and <10 Same-side interior 9) <11 and <16 Vertical Angles!! 10) <10 and <15 Alternate interior Determine relationship between the two angles. 4 1 2 3 5 8 6 7 11 12 10 9 16 13 14 15

  19. 11) <1 and <2 Linear pair! 12) <6 and <9 Alternate interior 13) <8 and <12 Same side interior Determine relationship between the two angles. 2 4 1 3 5 8 6 7 11 12 9 10 16 13 14 15

  20. 14) <2 and <5 Vertical Angles 15) <3 and <16 Alternate exterior 16) <8 and <16 corresponding Determine relationship between the two angles. 2 4 1 3 5 8 6 7 11 12 9 10 16 13 14 15

  21. 17) <6 and <3 Alternate interior 18) <11 and <15 Linear pair 19) <5 and <7 corresponding Determine relationship between the two angles. 3 2 4 1 5 8 7 6 11 12 9 10 16 13 14 15

  22. Name the transversal and the determine the relationships between the angles. 20) BCA and DGJ Line p, alt ext p q B F C t A D E G K s H J L

  23. Name the transversal and the determine the relationships between the angles. 20) BCA and DGJ Line p, alt ext p q B F 21) DGJ and FDE Line q, corresponding C t A D E G K s H J L

  24. Name the transversal and the determine the relationships between the angles. 20) BCA and DGJ Line p, alt ext 21) DGJ and FDE Line q, corresponding p q B F C t 22) FDE and KHL Line q, alt ext A D E G K s H J L

  25. Name the transversal and the determine the relationships between the angles. 20) BCA and DGJ Line p, alt ext 21) DGJ and FDE Line q, corresponding 22) FDE and KHL Line q, alt ext p q B F C t A D E G 23) DGJ and GJH Line p, alt int K s H J L

  26. Name the transversal and the determine the relationships between the angles. 20) BCA and DGJ Line p, alt ext 21) DGJ and FDE Line q, corresponding 22) FDE and KHL Line q, alt ext 23) DGJ and GJH Line p, alt int p q B F C t A D E G 24) CGH and GJH Line p, corresponding K s H J L

  27. Name the transversal and the determine the relationships between the angles. 20) BCA and DGJ Line p, alt ext 21) DGJ and FDE Line q, corresponding 22) FDE and KHL Line q, alt ext 23) DGJ and GJH Line p, alt int 24) CGH and GJH Line p, corresponding p q B F C t A D E G 25) BCA and CGH Line p, corresponding K s H J L

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