Download Chapter 3 Parallel and Perpendicular Lines

3.3.1 Prove Lines are Parallel
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In geometry we know rules about what angles
are formed by parallel lines, however this is not
as useful as the converse
When we did career projects we noticed it was
important to find angles in many situations,
these angles then tell us about the lines that
create them
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Consider the Corresponding Angles Postulate
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If two parallel lines are cut by a transversal then the
pairs of corresponding angles are congruent.
What if we knew about the angles and not the
lines, write the converse
Corresponding Angles Converse
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If two lines are cut by a transversal so that
corresponding angles are congruent then the lines
are parallel
•
If two lines are cut by a transversal so that
corresponding angles are congruent then the lines are
parallel
m
n
• So then we know that m||n
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What about the converse of our theorems that are
resultant of the Corresponding angles converse?
Alternate Interior Angles Theorem
 Alternate Exterior Angles Theorem
 Consecutive Interior Angles Theorem
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All have true and usable converses
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Two column Proof:
g
• Given 4  5
• Prove g || h
4
5
h
Statements
Reasons
1. 4  5
given
2. 1  4
Vertical Angles Congruence Theorem
3. 1  5
Transitive Property of Congruence
4. g || h
Corresponding Angles Converse
r
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Paragraph Proof:
Given: r || s and 1  3
Prove: p || q
s
p
3
2
1
• Let r || s and 1  3
• Since r || s then 1  2 because Corresponding
Angles are Congruent.
• Since 1  3 then, by transitive property of
congruence, 2 3.
• Since 2  3 and line p and q are cut by transversal r,
then p || q by Alternate Interior Angles Converse. //
q
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Given
p || q and q || r
Then
p || r
p
q
r
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P. 165
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1-16, 19-24, 28, 31, 34-37