Transcript is parallel to

Lines and Angles
Geometry
Chapter 3, Section 1
Notes
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What does it mean for two lines to be parallel?
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What about lines that do not intersect and are not
coplanar?
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Parallel lines: Lines that do not intersect and are coplanar.
Skew Lines: Lines that do not intersect and are not
coplanar.
What does it mean for two planes to be parallel?
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Parallel Planes: planes that do not intersect.
Example: the planes containing the ceiling and floor are
parallel
Notes
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Parallel Postulate:
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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.
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Parallel lines have the same slope (line P slope = 3 and Line
m slope = 3)
Tilted at the same angle
P
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Perpendicular Postulate:
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m
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.
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Perpendicular lines have slopes that are negative reciprocals
(line k slope = 4 and line Q slope = – 1/4)
Q
At 90 degrees from each other
k
Notes
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Transversal: a line that intersects two or
more lines in a plane at different points.
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E.g. Line c is a transversal to lines a and b.
Line b is a transversal to which two other lines?
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How about line a?
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a&c
When a transversal
intersects two lines,
how many angles are
formed?
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b
b&c
8 angles are formed
c
a
Notes
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Angles formed by a transversal.
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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
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Alternate Exterior Angles: 1 & 7 ; 2 & 8
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Congruent when the lines are parallel
Alternate Interior Angles: 3 & 5 ; 4 & 6
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Congruent when the lines are parallel
Congruent when the lines are parallel
Consecutive Interior Angles: 4 & 5 ; 3 & 6
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Supplementary when the lines are parallel
1 2
4 3
5 6
8 7
Notes
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Symbols for parallel in statements and figures
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The symbol ║ means is parallel to
The pink arrows on lines PQ and RS indicate that they
are parallel.
Parallel Line Problems
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1. Find the measure of each numbered angle
in the figure below.
Given:
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Line GH is parallel to ray DK
Angle 6 = 75 degrees.
Angle 2 = 30 degrees.