Geo 3.2 notes_parallel_converse
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3.1 Review: Angle Pairs 1 2 3 4 5 6 7 8 9 16 15 10 13 12 11 14 Corresponding Angles Alternate Int. Angles Consecutive Int. Angles ∠1 & ∠7 ∠3 & ∠5 ∠4 & ∠10 ∠13 & ∠15 ∠4 & ∠8 ∠3 & ∠7 ∠8 & ∠12 ∠3 & ∠9 ∠2 & ∠9 ∠3 & ∠8 ∠8 & ∠11 ∠14 & ∠15 1 Wednesday, October 13, 2010
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Review of Parallel Lines Theorems and their Converses.
Transcript of Geo 3.2 notes_parallel_converse
3.1 Review: Angle Pairs1 234
567 8
9 161510
13121114
Corresponding Angles
Alternate Int. Angles
Consecutive Int. Angles
∠1 & ∠7∠3 & ∠5
∠4 & ∠10∠13 & ∠15
∠4 & ∠8∠3 & ∠7
∠8 & ∠12∠3 & ∠9
∠2 & ∠9∠3 & ∠8
∠8 & ∠11∠14 & ∠15
1Wednesday, October 13, 2010
3.1 Review: Angle Pairs1 234
567 8
9 161510
13121114
Alternate Ext. Angles
Same-Side Ext. Angles
Vertical Angles
∠1 & ∠5∠2 & ∠6
∠16 & ∠12∠1 & ∠15
∠6 & ∠13∠6 & ∠1
∠5 & ∠2∠9 & ∠12
∠2 & ∠4∠3 & ∠1
∠11 & ∠13∠9 & ∠15
2Wednesday, October 13, 2010
Solve for the missing angles.∠1= 127° (linear with 53°)∠2=53° (vertical with 53°)∠3=127° (vertical with ∠1)∠5=53° (corr. with 53°)∠4=37° (comp. with ∠5)∠6=90° (vertical with rt. ∠)∠7=37° (corr. with ∠4)∠8=143° (linear with ∠7)∠9=37° (vertical with ∠7)∠10=143° (vertical with ∠8)
BM 14 and 15
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Solve for x and y.83 + x = 180 (Linear Pair)
x = 97°83 = y - 13 (alt.
ext. ∠s)y = 96°
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l
m
2 3
1
Prove the Alternate Exterior Angles TheoremGiven: m || l Prove: ∠1 ≅ ∠2
Statements Reasons
1. m || l 1. Given
2. ∠1 ≅ ∠3 2. Corr. ∠s are ≅
3. ∠3 ≅ ∠2 3. Vertical ∠s are ≅
4. ∠1 ≅ ∠2 4. Transitive
BM 16!!
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3.4 Proving Lines are Parallel
Benchmark 17
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What are Proofs?A “step-by-step” justification of what you are doing.Start with the given.Define what you know. (Statement, then Reason)End with your desired conclusion.
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Write the converse:If two lines are parallel, then their corresponding angles are congruent.
If two lines have corresponding angles congruent, then the lines are parallel.
Corresponding Angles Converse Postulate
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Write the converse:If two lines are parallel, then their alternate interior angles are congruent.
If two lines have alternate interior angles congruent, then the lines are parallel.
Alternate Interior Angles Converse Theorem
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Write the converse:If two lines are parallel, then their consecutive interior angles are supplementary.
If two lines have consecutive interior angles supplementary, then the lines are parallel.
Consecutive Interior Angles Converse Theorem
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Is it possible to show lines m and n are parallel? Why?
m
50°
50°
n
Ex. 1:
Yes, Alternate Interior Angles
ConverseEx. 2:
m
80°100°
n
Yes, Consecutive Interior Angles
Converse
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What value makes these lines parallel?
4x + 4°
92°
•These angles are alternate exterior angles
•If alternate exterior angles are congruent (equal), then the lines are parallel
4x + 4 = 924x = 88x = 22
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BM #13: Proving Parallel Lines
Given the angle relationship, which lines are parallel and why?
Ex. 3: ∠1≅∠5a || b by alt. ext. converse
1 234
567 8
9 161510
13121114
a
b
cd
Ex. 4: ∠8≅∠12c || d by alt. int. converse Ex. 5: ∠2 and ∠9 are
supplementaryc || d by con. int. converse
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Summary:The Angle Theorems state “If lines are parallel, then angles are ≅ or supplementary.”The Converse Theorems state “If angles are ≅ or supplementary, then the lines are parallel.”
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Assignment:
#18 3-2 WS p. 295 (Due at the end of class)#19 p. 137 ##1-9 (odd), 10-20 (all), 26, 27, 30, 51, 52, 56-62 (even)
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