Chapter 3.3 Notes: Prove Lines are Parallel - PowerPoint PPT Presentation

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Chapter 3.3 Notes: Prove Lines are Parallel

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Chapter 3.3 Notes: Prove Lines are Parallel Goal: You will use angle relationships to prove that lines are parallel. Postulate 16 Corresponding Angles Converse: If ... – PowerPoint PPT presentation

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Title: Chapter 3.3 Notes: Prove Lines are Parallel


1
Chapter 3.3 Notes Prove Lines are Parallel
  • Goal You will use angle relationships to prove
    that lines are parallel.

2
  • Postulate 16 Corresponding Angles Converse
  • If two lines are cut by a transversal so that
    corresponding angles are congruent, then the
    lines are parallel.
  • Ex.1 Find the value of x that makes mn.

3
  • Ex.2 Is there enough information in the diagram
    to conclude that mn? Explain.
  • Theorem 3.4 Alternate Interior Angles Converse
  • If two lines are cut by a transversal so that
    alternate interior angles are congruent, then the
    lines are parallel.

4
  • Theorem 3.5 Alternate Exterior Angles Converse
  • If two lines are cut by a transversal so that
    alternate exterior angles are congruent, then the
    lines are parallel.
  • Theorem 3.6 Consecutive Interior Angles Converse
  • If two lines are cut by a transversal so that
    consecutive interior angles are supplementary,
    then the lines are parallel.

5
  • Can you prove that lines a and b are parallel?
    Explain why or why not.
  • Ex.3 Ex.4
  • Ex.5

6
  • Ex.6 Find the value of y that makes ab.
  • (5y 6)o
  • 121o

7
  • Ex.7 Given
  • Prove pq

8
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9
  • Ex.8 Given
  • Prove r p

10
  • Ex.9
  • Given
  • Prove

11
  • Ex.10
  • Given
  • Prove and are supplementary.

  • 1 p

  • 3
  • 2
    q

12
  • Ex.11
  • Given are
    supplementary
  • Prove l m

13
  • Ex.12
  • Given
  • Prove
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