3.2

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3.2 Use Parallel Lines and Transversals

• Postulate 15 Corresponding Angles Postulate
• If two parallel lines are cut by a transversal,
  then the pairs of corresponding angles are
  congruent.

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3.2 Use Parallel Lines and Transversals

• Example 1 Identify congruent angles
• The measure of three of the numbered angles is 55
  degrees. Identify the angles. Explain your
  reasoning.
• What are the measures of the
• other angles in the picture?

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3.2 Use Parallel Lines and Transversals

• Theorem 3.1 Alternate Interior Angles Theorem
• If two parallel lines are cut by a transversal,
  then the pairs of alternate interior angles are
  congruent.

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3.2 Use Parallel Lines and Transversals

• Theorem 3.1 Alternate Exterior Angles Theorem
• If two parallel lines are cut by a transversal,
  then the pairs of alternate exterior angles are
  congruent.

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3.2 Use Parallel Lines and Transversals

• Theorem 3.1 Consecutive Interior Angles Theorem
• If two parallel lines are cut by a transversal,
  then the pairs of consecutive interior angles are
  supplementary.

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3.2 Use Parallel Lines and Transversals

• Example 2 Use properties of parallel lines
• Find the value of x.

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3.2 Use Parallel Lines and Transversals

• Example 3 Use properties of parallel lines
• Find the value of x.

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3.2 Use Parallel Lines and Transversals

• Example 4 Use properties of parallel lines
• Find the value of x.

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3.2 Use Parallel Lines and Transversals

• Example 5 Use properties of parallel lines
• Find the value of x and y.

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3.2 Use Parallel Lines and Transversals

• Example 6 Use properties of parallel lines
• Find the value of x and y.

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3.2 Use Parallel Lines and Transversals

• Example 7 Use properties of parallel lines
• Find the value of x and y.

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3.2 Use Parallel Lines and Transversals

• Example 8 Prove the Alternate Interior Angles
  Theorem
• Prove that if two parallel lines are cut by a
  transversal, then the pairs of alternate interior
  angles are congruent.

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3.2 Use Parallel Lines and Transversals

• Example 9 Solve a real world problem.
• When sunlight enters a drop of rain, different
  colors of light leave the drop at different
  angles. This process is what makes a rainbow.
  For violet light, mlt2 40 degrees. What is
  mlt1? How do you know?