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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!