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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 . What about lines that don’t intersect and aren’t coplanar?

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lines and angles

Lines and Angles

Geometry

Chapter 3, Section 1

notes
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 don’t intersect and aren’t 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
notes3
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 (e.g. slope of 3 and 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 (e.g. 4 and – 1/4)
      • At 90 degrees from each other
notes4
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
notes5
Notes
  • Angles formed by a transversal.
      • We give certain pairs of these angles special names.
      • Corresponding Angles: 1 & 5 ; 2 & 6 ; 3 & 7 ; 4 & 8
      • Exterior Angles: 1, 2, 7, & 8
      • Interior Angles: 3, 4, 5, 6
      • Alternate Exterior Angles: 1 & 7 ; 2 & 8
      • Alternate Interior Angles: 3 & 5 ; 4 & 6
      • Consecutive Interior Angles: 4 & 5 ; 3 & 6
notes6
Notes
  • Symbols for parallel in statements and figures
      • The symbol ll means is parallel to
      • The pink arrows on lines PQ and RS indicate that they are parallel.
angle pair names activity
Angle Pair Names Activity
  • Using about ¼ of a piece of binder paper, draw three lines so that one intersects two of the others.
    • Color the exterior angles all one color
    • Color the interior angles all one color
    • Label the exterior and interior angles
  • Using another ¼ of a piece of binder paper, draw three lines so that one intersects two of the others.
    • Color each pair of corresponding angles a different color.
    • Label this quarter sheet of paper “corresponding angles.”
  • Using another ¼ of a piece of binder paper, draw three lines so that one intersects two of the others.
    • Color each pair of alternate exterior angles a different color.
    • Color each pair of alternate interior angles a different color.
    • Label this quarter sheet “alternate exterior and interior angles.”
  • Using the final ¼ of a piece of binder paper, draw three lines so that one intersects two of the others.
    • Color each pair of consecutive interior angles a different color.
    • Label this quarter sheet “consecutive interior angles.
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