Section 3-3 Proving Lines Parallel – Day 1, Calculations. Michael Schuetz.
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Transcript of Section 3-3 Proving Lines Parallel – Day 1, Calculations. Michael Schuetz.
![Page 1: Section 3-3 Proving Lines Parallel – Day 1, Calculations. Michael Schuetz.](https://reader036.fdocuments.in/reader036/viewer/2022082620/5a4d1b2e7f8b9ab059999f02/html5/thumbnails/1.jpg)
Section 3-3Proving Lines Parallel –Day 1, Calculations.Michael Schuetz
![Page 2: Section 3-3 Proving Lines Parallel – Day 1, Calculations. Michael Schuetz.](https://reader036.fdocuments.in/reader036/viewer/2022082620/5a4d1b2e7f8b9ab059999f02/html5/thumbnails/2.jpg)
Theorem 3-4: Converse of the Corresponding Angles Theorem.Theorem
If
Then
If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.
lm
2
6
2 6
||l m
![Page 3: Section 3-3 Proving Lines Parallel – Day 1, Calculations. Michael Schuetz.](https://reader036.fdocuments.in/reader036/viewer/2022082620/5a4d1b2e7f8b9ab059999f02/html5/thumbnails/3.jpg)
Theorem 3-5: Converse of the Alternate Interior Angles Theorem.
Theorem If
Then
If two lines and a transversal form alternate interior angles that are congruent, then the lines are parallel.
lm
46
4 6
||l m
![Page 4: Section 3-3 Proving Lines Parallel – Day 1, Calculations. Michael Schuetz.](https://reader036.fdocuments.in/reader036/viewer/2022082620/5a4d1b2e7f8b9ab059999f02/html5/thumbnails/4.jpg)
Theorem 3-6: Converse of the Same-Side Interior Angles Postulate.
Theorem If
Then
If two lines and a transversal form same-side interior angles that are supplementary, then the lines are parallel.
lm
36
3 6 180m m
||l m
![Page 5: Section 3-3 Proving Lines Parallel – Day 1, Calculations. Michael Schuetz.](https://reader036.fdocuments.in/reader036/viewer/2022082620/5a4d1b2e7f8b9ab059999f02/html5/thumbnails/5.jpg)
Theorem 3-7: Converse of the Alternate Exterior Angles Theorem.
Theorem If
Then
If two lines and a transversal form alternate exterior angles that are congruent, then the lines are parallel.
lm
1
7
1 7
||l m
![Page 6: Section 3-3 Proving Lines Parallel – Day 1, Calculations. Michael Schuetz.](https://reader036.fdocuments.in/reader036/viewer/2022082620/5a4d1b2e7f8b9ab059999f02/html5/thumbnails/6.jpg)
Example 1, Identifying parallel lines Which lines are parallel if
and ? Justifies your answers?
lm
12
43
5
6
8
7
p q
9
Converse of the corresponding angles theorem
/ /p q
3 8 1 4
3 8
Converse of the alternate interior angles theorem
/ /l m1 4
![Page 7: Section 3-3 Proving Lines Parallel – Day 1, Calculations. Michael Schuetz.](https://reader036.fdocuments.in/reader036/viewer/2022082620/5a4d1b2e7f8b9ab059999f02/html5/thumbnails/7.jpg)
Example 2, Using Algebra What is the value of x that makes p//q? Which
theorem or postulate justifies your answer?
lp q
2x+9˚ 2 189 0111o oox
The converse of the Same-Side Interior Postulate tells us that to make p//q, then111˚2 120 180o o ox
2 60ox 30ox
![Page 8: Section 3-3 Proving Lines Parallel – Day 1, Calculations. Michael Schuetz.](https://reader036.fdocuments.in/reader036/viewer/2022082620/5a4d1b2e7f8b9ab059999f02/html5/thumbnails/8.jpg)
Homework: Day 1 P. 160, #’s 7, 8, 15, 16, 27, 28, 31, 32,
47, 48
![Page 9: Section 3-3 Proving Lines Parallel – Day 1, Calculations. Michael Schuetz.](https://reader036.fdocuments.in/reader036/viewer/2022082620/5a4d1b2e7f8b9ab059999f02/html5/thumbnails/9.jpg)
Section 3-3Proving Lines Parallel –Day 2, Proofs.
Michael Schuetz
![Page 10: Section 3-3 Proving Lines Parallel – Day 1, Calculations. Michael Schuetz.](https://reader036.fdocuments.in/reader036/viewer/2022082620/5a4d1b2e7f8b9ab059999f02/html5/thumbnails/10.jpg)
Proof of Theorem 3-5: Given: Prove: l//m
4 6 lm
42
6Statements Reasons
1. Given
4. / /l m
2. 2 4 2. Vertical angles are congruent3. 2 6 3. Transitive property
1. 4 6
4. Theorem 3-4: If corresponding angles are congruent then the lines are parallel.
![Page 11: Section 3-3 Proving Lines Parallel – Day 1, Calculations. Michael Schuetz.](https://reader036.fdocuments.in/reader036/viewer/2022082620/5a4d1b2e7f8b9ab059999f02/html5/thumbnails/11.jpg)
Proof of Theorem 3-7: Given: Prove: l//m
1 7 lm
31
7Statements Reasons
1. Given
4. / /l m
2. 3 1 2. Vertical angles are congruent3. 3 7 3. Transitive property
1. 1 7
4. Theorem 3-4: If corresponding angles are congruent then the lines are parallel.
![Page 12: Section 3-3 Proving Lines Parallel – Day 1, Calculations. Michael Schuetz.](https://reader036.fdocuments.in/reader036/viewer/2022082620/5a4d1b2e7f8b9ab059999f02/html5/thumbnails/12.jpg)
Proof of Theorem 3-4: Given: Prove: l//m
1 5 lm 5
14
Statements Reasons
1. Given
4. / /l m
02. m 1 4 180m 2. Angles 1 and 4 form a linear pair3. Substitution
1. 1 5
4. Theorem 3-6: If same-side interior angles are supplementary then the lines are parallel.
03. m 5 4 180m
![Page 13: Section 3-3 Proving Lines Parallel – Day 1, Calculations. Michael Schuetz.](https://reader036.fdocuments.in/reader036/viewer/2022082620/5a4d1b2e7f8b9ab059999f02/html5/thumbnails/13.jpg)
Homework: Day 2 P. 161, #’s 17-26, for 40 & 41 write a 2
column proof.