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 Objectives You can use certain angle pairs to determine if two lines are parallel ID: 659381
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Slide1
3-3 Proving Lines ParallelSlide2
Students will be able to
Determine whether two lines are parallel
Write flow proofsDefine and apply the converse of the theorems from the previous section
ObjectivesSlide3
You can use certain angle pairs to determine if two lines are parallel
Essential UnderstandingSlide4
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 parallelSlide5
Which lines are parallel if <6
≅
<7?m ||
l
Which lines are parallel if <4
≅
<6
a ||
b
Identifying Parallel LinesSlide6
If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel
Converse of the Alternate Interior Angles TheoremSlide7
If two lines and a transversal form same side interior angles that are supplementary, then the two lines are parallel.
Converse of the Same-Side Interior Angles TheoremSlide8
If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel.
Converse of the Alternate Exterior Angles TheoremSlide9
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 parallelIf same side interior angles are supplementary, then the lines are parallel
SummarySlide10
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
Things to Keep in Mind…Slide11
Third way to write a proofIn a flow proof, arrows show the flow, or the logical connections, between statements.
Reasons are written below the statements
Flow ProofSlide12
Given: <4
≅
<6Prove: l
||
m
Proof of the Converse of Alternate Interior Angles Theorem
<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 parallelSlide13
Given: m
<5 = 40,
m<2 = 140Prove: 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
Write a flow proofSlide14
Given:
m
<5 = 40, m<2 = 140
Prove: a ||
b
Write a flow proof
<5 = 40
Given
<2
= 140
Given
<5 and <2 are Supp. <
s
Def. of Supp. <
s
<5 and <2 are Same side Interior Angles
Def. of Same Side Interior <
s
a ||
b
Converse of Same Side Int. <
s
ThmSlide15
You now have four ways to prove if two lines are parallelSlide16
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
Using AlgebraSlide17
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
Using AlgebraSlide18
Pg. 160 – 162# 7 – 16, 21 – 24, 28, 32
16 Problems
Homework