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## Lesson 3-3: Proving Lines Parallel

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### Lesson 3-3: Proving Lines Parallel Today s Learning Goals: Which theorem proves two lines are parallel? How do I set up an equation to solve for the x-value that ... – PowerPoint PPT presentation

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Title: Lesson 3-3: Proving Lines Parallel

1
Lesson 3-3 Proving Lines Parallel
• Todays Learning Goals
• Which theorem proves two lines are parallel?
• How do I set up an equation to solve for the
x-value that will make two lines parallel?

2
Review
• 1. Solve for x.
• 2. What is a converse to a conditional statement?

3
Postulate 3-2 Converse of the Corresponding
Angles Postulate
• Corresponding Angles postulate states If lines
cut by a transversal are parallel, then the
corresponding angles are congruent.
• Corresponding Angles Converse If lines cut by a
transversal form corresponding angles that are
congruent, then
• the lines are parallel.

4
Example Which lines are parallel? Justify your
• 1) If ?
• 2) If ?

5
Converses to the other Angle Theorems
• Alternate Interior Angles Theorem Converse If
alternate interior angles are congruent, then the
lines are parallel.
• Alternate Exterior Angles Theorem Converse If
alternate exterior angles are congruent, then the
lines are parallel.

6
Converses to the other Angle Theorems
• Same-Side Interior Angles Theorem Converse If
same-side interior angles are supplementary, then
the lines are parallel.
• Same-Side Exterior Angles Theorem Converse If
same-side exterior angles are supplementary, then
the lines are parallel.

7
Proof Alternate Interior Angles Converse
• Statements Reasons
• 1. 1.
• 2. 2.
• 3. 3.
• 4. 4.

Given
Vertical Angles Theorem
Transitive Property of
Corresponding Angles Converse
8
Proof Same-Side Exterior Angles Converse
• Statements Reasons
• 1. 1.
• 2. 2.
• 3. 3.
• 4. 4.

Given
Vertical Angles Theorem
Transitive Property of
Corresponding Angles Converse
9
Example Are the lines parallel?
• If , are lines r and s parallel?

10
Last Example! Solving for X
• What value of x would make the lines parallel?
• a) b)

11
Recap Theorems vs Converses
• The angle pair THEOREMS
• Given - lines are parallel
• Conclusion angle pairs are or
supplementary
• Angle pair CONVERSES
• Given - angle pairs are or supplementary
• Conclusion lines are parallel

12
3-3 Classwork
• You may work with a partner, no changing seats.