Transcript Chapter 3 Parallel and Perpendicular Lines

Chapter 3
Parallel and Perpendicular Lines
3.1 Identify Pairs of Lines and Angles
New in this Section:
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So far we have looked at angle pairs formed by 2
lines
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Vertical angles
Supplemental angles
Complementary angles
Now we will look at angle pairs formed by 3
lines
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Interior angles
 Same side (consecutive)
 Alternate interior
Exterior angles
Corresponding angles
Euclidean Geometry
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High School Geometry, invented by a Greek
mathematician Euclid is based on 5 principals
known as postulates
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We know them they are easy
A line can be drawn between 2 points
 Any line segment can be a line
 Circles exist with a given radius
 All right angles are congruent
 Parallel lines exist
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In this section we will study the 5th postulate,
presented in our book as postulate 13
The world of Geometry
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Everything in geometry that we do in high
school is proven based on the idea that these 5
postulates are fact
1-4 are easy to prove
5 is not, in fact it has never been proven!
This is why many forms of geometry exist!
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Global Geometry!
Why is Euclid’s Geometry so popular?
Every line that does not intersect is
either Parallel or Skew!
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Skew lines do not intersect but do not exist in
the same plane
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Think of a cube, the top of the front face and the bottom of the
rear face
Parallel lines are lines that do not intersect and
exist in the same plane
How many pairs of parallel sides?
How
many pairs of perpendicular sides?
Transversal
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Any line that intersects two other lines
L
n
m
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Discussion: which line is the transversal?
Postulate 13(Euclid’s
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th
5 )
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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Ex. There is exactly one line through P parallel to line L.
P
Line
parallel To
line L
Any other line is
not parallel
L
Perpendicular Postulate
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Same idea as 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 perpendicular to the
given line
Ex. There is exactly one line through P perpendicular to line L.
Line Perpendicular
To line L
P
Any other line is
not perpendicular
L
Symbolic Representations
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AB || CD
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Translation: line AB is parallel to line CD
n
m
L
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Translation line n is parallel to line m
Two arrow heads are
the symbol here
Symbolic Representations
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AB ┴ CD
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Translation: line AB is perpendicular to line CD
m
The square is the
symbol here
n
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Translation: line n is perpendicular to line m
Homework
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P. 150
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1-10, 24-28, 34-37