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Planes, Lines and Transversals
 

Planes, Lines and Transversals

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    Planes, Lines and Transversals Planes, Lines and Transversals Presentation Transcript

    • PARALLEL LINES IN A PLANE
    • ParallelandSkewLines
    • pgs 77-78
      Parallel lines are coplanar lines that do not intersect.
      AB || GH
      Skew lines are non-coplanar lines which are neither parallel nor intersecting.
      AB and HI are skew
      Parallel planes are planes that do not intersect.
      plane ABCD || plane GHIJ
      Two segments and/or rays are parallel if and only if the lines containing them are also parallel.
      AB || GH
    • pg 78
      TRANSVERSALS
      A line is a transversal if and only if it intersects two or more coplanar lines at different points.
      referred to as “cutting” the lines
      How many angles formed?
      x
      f
      g
      y
      h
    • pg 79
      Exterior
      1
      2
      f
      3
      4
      Interior
      g
      5
      6
      8
      7
      Exterior
      h
      Interior – region whose boundaries include the lines
      Exterior – region which has only one of the lines as its lone boundary
      Interior angles: 3, 4, 5, 6
      Exterior angles: 1, 2, 7, 8
    • pg 80
      1
      2
      3
      4
      5
      6
      7
      8
    • EXAMPLE:
      4
      3
      2
      1
      8
      7
      6
      5
      Give all the corresponding angles.
      1 and 3 2 and 4
      5 and 7 6 and 8
      Give all the alternate interior angles.
      2 and 7 3 and 6
      3. Give all the alternate exterior angles.
      1 and 8 4 and 5
    • 4
      5
      9
      6
      3
      2
      7
      8
      Use the figure above and identify the following pairs (next slide) whether they are one of the following:
      Corresponding angles
      Alternate interior angles
      Alternate exterior angles
      Vertical angles
      Linear pair
    • Two angles are called vertical angles if and if only they are two nonadjacent angles formed by two intersecting lines.
      Two angles form a linear pair if and only if the angles are adjacent and the non-common sides form opposite rays.
      2
      VERTICAL ANGLES:
      • 1 and 3
      • 2 and 4
      1
      3
      4
      LINEAR PAIRS:
      • 1 and 2
      • C and D
      D
      2
      C
      1
    • Corresponding angles
      Alternate interior angles
      Alternate exterior angles
      Vertical angles
      Linear pair
      4
      5
      9
      6
      3
      2
      7
      8
      9 and 3 - Alternate exterior angles
      5 and 7 - Alternate interior angles
      7 and 9 - Vertical angles
      6 and 2 - Alternate interior angles
      4 and 6 - Corresponding angles
      2 and 8 - Corresponding angles
      5 and 4 - Linear Pair