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Lines and Angles

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Lines and Angles Geometry Chapter 3, Section 1 Notes What does it mean for two lines to be parallel? Parallel lines: Lines that do not intersect and are coplanar. – PowerPoint PPT presentation

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Title: Lines and Angles


1
Lines and Angles
  • Geometry
  • Chapter 3, Section 1

2
Notes
  • What does it mean for two lines to be parallel?
  • Parallel lines Lines that do not intersect and
    are coplanar.
  • What about lines that do not intersect and are
    not coplanar?
  • Skew Lines Lines that do not intersect and are
    not coplanar.
  • What does it mean for two planes to be parallel?
  • Parallel Planes planes that do not intersect.
  • Example the planes containing the ceiling and
    floor are parallel

3
Notes
  • Parallel Postulate
  • If there is a line and a point not on the line,
    then there is exactly one line through the point
    parallel to the given line.
  • Parallel lines have the same slope (line P slope
    3 and Line m slope 3)
  • Tilted at the same angle
  • Perpendicular Postulate
  • If there is a line and a point not on the line,
    then there is exactly one line through the point
    perpendicular to the given line.
  • Perpendicular lines have slopes that are negative
    reciprocals (line k slope 4 and line Q slope
    1/4)
  • At 90 degrees from each other

4
Notes
  • Transversal a line that intersects two or
  • more lines in a plane at different points.
  • E.g. Line c is a transversal to lines a and b.
  • Line b is a transversal to which two other lines?
  • a c
  • How about line a?
  • b c
  • When a transversal
  • intersects two lines,
  • how many angles are
  • formed?
  • 8 angles are formed

5
Notes
  • Angles formed by a transversal.
  • We give certain pairs of these angles special
    names.
  • Exterior Angles 1, 2, 7, 8
  • Interior Angles 3, 4, 5, 6
  • Corresponding Angles 1 5 2 6 3 7 4
    8
  • Alternate Exterior Angles 1 8 2 7
  • Alternate Interior Angles 3 6 4 5
  • Consecutive Interior Angles 4 6 3 5

6
Notes
  • Symbols for parallel in statements and figures
  • The symbol means is parallel to
  • The pink arrows on lines PQ and RS indicate that
    they are parallel.

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