3.2 Angles and Parallel Lines
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Transcript of 3.2 Angles and Parallel Lines
8/8/2019 3.2 Angles and Parallel Lines
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ObjectivesObjectives Use the properties of
parallel lines to determine
congruent angles
Use algebra to find
angle measures
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Postulate 3.1
Corresponding s Postulate If 2±± lines are cut by a
transversal, then each
pair of corres. s is $.
i.e. If l ±±m , then 1$2.
l
m
1
2
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Answer:
Corresponding Angles Postulate
Vertical Angles Theorem
Transitive Property
Definition of congruent angles
Substitution
In the figure andFind
Example 1:Example 1:
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Answer:
In the figure and Find
Your Turn:Your Turn:
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Theorem 3.1Theorem 3.1
Alternate Interior Alternate Interior s Theorems Theorem If 2±± lines are cut by a transversal, then
each pair of alternate interior s is $.
i.e. If l ±±m , then 1$2.
l
m
1
2
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Proof of Alt. Int.Proof of Alt. Int. s Theorems Theorem
Statements1. l ±±m
2. 3 $ 2
3. 1 $ 3
4. 1 $ 2
Reasons1. Given
2. Corresponding s post.
3. Vert. s Thm
4. $ is transitive
l
m
1
2
3
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Theorem 3.2Theorem 3.2
Consecutive Interior Consecutive Interior s Theorems Theorem If 2±± lines are cut by a transversal, then
each pair of consecutive int. s is
supplementary.
i.e. If l ±±m , then 1 & 2 are supplementary or m1 + m2 =
180°.
l
m 1
2
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Theorem 3.3Theorem 3.3
Alternate Exterior Alternate Exterior s Theorems Theorem If 2±± lines are cut by a transversal, then
the pairs of alternate exterior s are $.
i.e. If l ±±m , then 1$2.
l m
1
2
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If a transversal is B to one of 2 ±± lines,
then it is B to the other.
i.e. If l ±±m , & t B l , then t Bm .
1
2
Theorem 3.4B
Transversal Theorem
l
m
t
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Proof of B Transversal Theorem
Statements
1. l ±±m , t B l
2. 1$2
3. m1=m2
4. 1 is a rt.
5. m1 = 90o
6. 90o = m2
7. 2 is a rt.
8 . t Bm
Reasons
1. Given
2. Corresp. s post.
3. Def of $ s
4. Def of B lines
5. Def of rt.
6. Substitution prop =
7. Def of rt.
8. Def of B lines
1
2
l
m
t t
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Find:
m1 =
m2 =m3 =
m4 =
m5 =
m6 =
x =
125o 2
1
3
4 6
5
x+15o
5555°°
125125°°5555°°
125125°°
5555°°
125125°°
4040°°
Example 2:Example 2:
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What is the measure of RTV ?
Example 3:Example 3:
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Angle AdditionPostulate
Definition of congruentangles
Substitution
Alternate Interior AnglesTheorem
Answer: RTV = 125°
Example 3:Example 3:
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Definition of congruent angles
Substitution
Subtract x from each side and
add 10 to each side.
Definition of congruent angles
Substitution
Find y .
by the Alternate Exterior AnglesTheorem.
Example 4:Example 4:
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Simplify.
Add 100 to each side.
Divide each side by 4.
Answer:
Example 4:Example 4:
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Answer:
ALGEBRA If andfind x and y .
Your Turn: Your Turn:
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AssignmentAssignment Geometry:
Pg. 136 ± 138 #5 ± 27, 32, 34
Pre-AP Geometry:
Pg. 136 ± 138 #14 - 39
