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Slope and Parallel Lines

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Slope and Parallel Lines Sections 4.5 & 4.6 Definitions A plane is a surface such that if any two points on the surface are connected by a line, all points of the ... – PowerPoint PPT presentation

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Title: Slope and Parallel Lines


1
Slope and Parallel Lines
  • Sections 4.5 4.6

2
Definitions
  • A plane is a surface such that if any two points
    on the surface are connected by a line, all
    points of the line are also on the surface.
  • A plane has only two dimensions length and
    width but no thickness.

3
Definitions
  • If points, lines, segments, and so forth lie in
    the same plane, we call them coplanar.
  • Points, lines, segments, and so forth that do not
    lie in the same plane are called noncoplanar.

4
Definitions
  • A transversal is a line that intersects two
    coplanar lines in two distinct points.

5
(No Transcript)
6
Definitions
  • In the diagram, the region between lines d and e
    is the interior of the figure.
  • In the diagram, the rest of the plane except the
    region between lines d and e is the exterior of
    the figure.

7
Definitions
  • Alternate Interior Angles are a pair of angles
    formed by two lines and a transversal. The angles
    must
  • both lie in the interior of the figure,
  • lie on alternate sides of the transversal,
  • have different vertices.

8
Definitions
  • Alternate Exterior Angles are a pair of angles
    formed by two lines and a transversal. The angles
    must
  • both lie in the exterior of the figure,
  • lie on alternate sides of the transversal,
  • have different vertices.

9
Definitions
  • Corresponding Angles are a pair of angles formed
    by two lines and a transversal.
  • One angle must lie in the interior of the figure,
    and the other must lie in the exterior.
  • The angles must lie on the same side of the
    transversal but have different vertices.

10
corr. angles
alt. ext. angles
alt. int. angles
corr. angles
vert. angles
corr. angles
alt. ext. angles
alt. int. angles
11
Name the pairs of...
12
Parallel Lines
  • Parallel () lines are two coplanar lines which
    do not intersect.
  • Parallel lines have the same slope.

13
Slope Review ?
  • The slope of a nonvertical line (or segment or
    ray) containing points (x1, y1) and (x2, y2) is
    defined by
  • Find the slope of the line containing points (2,
    -1) and (7, 4)

14
Remember,
  • Rising line positive slope
  • Falling line negative slope
  • Horizontal line zero slope
  • Vertical line no slope (undefined slope)

15
Slopes of Parallel Lines
  • Theorem 26 If two nonvertical lines are
    parallel, then their slopes are equal.
  • Theorem 27 If the slopes of two nonvertical
    lines are equal, then the lines are parallel.

Note You do NOT need to prove these theorems!!
16
Slopes of Perpendicular Lines
Note You do NOT need to prove these theorems!!
  • Theorem 28 If two nonvertical lines are
    perpendicular, then each lines slope is the
    opposite reciprocal of the others.
  • Theorem 29 If a lines slope is the opposite
    reciprocal of another lines slope, then the two
    lines are perpendicular.

Flip the top and bottom of fraction and change to
opposite sign!
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