Notes 3.3: Proving Lines Parallel
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Follow along and fill in the missing blanks for each theorem. lben, based on the theorem, use the
given theorem to determine if the lines are parallel or not parallel. hovide 3gsssning.
:
If 2 lines are cut by a trarisversal
corresponding angles are
,
so
the
then the lines are
Non Example:
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r
ffiAnglesConverseTheorem:If2linesarecutbyatransversalsothe
alternate interior angles are
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then the lines
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@sConverseTlreorem:If.2linesarecutbyatransversalsothe
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then the lines arc PqrJ lL-l
alternate exterior angles arc hxg"r*,
Examplo
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Consecutive Exterior Angles Converse Theorem: If 2 lines are cut by a tra
then the lines are
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Is it possible to prove the lines are parallel or not parallel? If so, state the postulate or
theorem you would use. If not, state cannot be determined.
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10. Find the value of
xthat
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b: EInd thevalue of ythat makes
xtbat makes a llb.
= l8o-
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c. Is b
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Stati'the pcrbtulate or theorem that supports each conclusion.
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Conelusion: 12 z
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2. Given:'m14*mZ7=180
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Conclusion:allb
3. Given: 14= Z5
Conclusion:allb
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Find the values of x and y. Explain your reasoning by stating the proper theorem or
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5.
y= l15
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Find the value of x
solution.
so
x=
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g,X- Ig +-Bx-S =t8o
ffi*")fl,
lZx4l =rc9
t2.3
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ID =V4
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x=9
z=
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Can you prove that lines p and q are parallel?
would use.
10.
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Pra
TE
K=
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tbat a I I m. State the theorem or postulate that justifres your
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x= l0o
Linex
.
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If
so, state
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l9.b
1(
=19.b
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the theorem or postulate that
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