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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
answer.
  • 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?
    Justify your answer.

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.
  • Heading
  • 3-3 Classwork pg 169 1, 2, 7, 9, 14, 19, 20,
    22, 23, 24
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