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Students will be able to
◦ Determine whether two lines are parallel
◦ Write flow proofs
◦ Define and apply the converse of the theorems from the previous section

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You can use certain angle pairs to determine if two lines are parallel

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What is the corresponding angles theorem?
If a transversal intersects two parallel lines, then corresponding angles are congruent
What is the converse of the corresponding angles theorem?
If two lines and a transversal form congruent corresponding angles, then the lines are parallel

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Which lines are parallel if <6 ≅ <7?
◦ m || l
Which lines are parallel if <4 ≅ <6
◦ a || b

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If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel

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If two lines and a transversal form same side interior angles that are supplementary, then the two lines are parallel.

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If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel.

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If corresponding angles are congruent, then the lines are parallel
If alternate interior lines are congruent, then the lines are parallel
If alternate exterior lines are congruent, then the lines are parallel
If same side interior angles are supplementary, then the lines are parallel

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In order to use the theorems relating to parallel lines, you must first prove the lines are parallel if it is not given/stated in the problem.
Even if lines appear to be parallel, you cannot assume they are parallel
Always assume diagrams are NOT drawn to scale, unless otherwise stated

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Third way to write a proof
In a flow proof, arrows show the flow, or the logical connections, between statements.
Reasons are written below the statements

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Given: <4 ≅ <6
Prove: l || m
<4 ≅ <6
Given
<2 ≅ <4
Vert. <s are ≅
<2 ≅ <6
Trans. Prop of ≅
L || m
Converse of
Corresponding
Angles Thm.
*You cannot use the Corresponding Angles Thm to say
<2 ≅ <6 because we do not know if the lines are parallel

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Given: m<5 = 40, m<2 = 140
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Prove: a || b
Start with what you know
◦ The given statement
◦ What you can conclude from your picture.
What you need to know
◦ Which theorem you can use to show a||b

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Given: m<5 = 40, m<2 = 140
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Prove: a || b
<5 = 40
Given
<5 and <2 are
Supp. <s
Def. of Supp. <s
<2 = 140
Given <5 and <2 are
Same side Interior
Angles
Def. of Same
Side Interior <s a || b
Converse of
Same Side
Int. <s Thm

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You now have four ways to prove if two lines are parallel

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What is the value of x for which a || b?
Work backwards. What must be true of the given angles for a and b to be parallel?
How are the angles related?
◦ Same side interior
◦ Therefore, they must add to be 180

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What is the value of x for which a || b?
Work backwards. What must be true of the given angles for a and b to be parallel?
How are the angles related?
◦ Corresponding Angles
◦ Therefore, the angles are congruent

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Pg. 160 – 162
# 7 – 16, 21 – 24, 28, 32
16 Problems