3-2 Properties of Parallel Lines

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3-2 Properties of Parallel Lines
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Congruent Angle Relationships

• Corresponding Angles Postulate If a transversal
  intersects two parallel lines, then corresponding
  angles are congruent.
• Alternate Interior Angles Theorem If a
  transversal intersects two parallel lines, then
  alternate interior angles are congruent.
• Alternate Exterior Angles Theorem If a
  transversal intersects two parallel lines, then
  alternate exterior angles are congruent.

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Identifying Congruent Angles

• Which angles measure 55?? How do you know?

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? If m?4 50, what is m?6?
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Other Angle Relationships

• Same-Side Interior Angles Theorem If a
  transversal intersects two parallel lines, then
  same-side interior angles are supplementary.

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Finding Measures of Angles

• What are the measures of each angle? Justify
  each answer.

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Finding an Angle Measure

• What is the value of y?

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3-3 Proving Lines Parallel
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Converse

• A statement in the form If, then is called a
  conditional statement.
• If you work hard, then you will have good grades.
• When the if and then parts are switched, it
  is called the converse of the statement.
• If you have good grades, then you worked hard.

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Converses of Postulates and Theorems

• Converse of the Corresponding Angles Postulate
  If two lines and a transversal form corresponding
  angles that are congruent, then the lines are
  parallel.
• Converse of the Alternate Interior Angles
  Theorem If two lines and a transversal form
  alternate interior angles that are congruent,
  then the two lines are parallel.
• Converse of the Same-Side Interior Angles
  Theorem If two lines and a transversal form
  same-side interior angles that are supplementary,
  then the lines are parallel.
• Converse of the Alternate Exterior Angles
  Theorem If two lines and a transversal form
  alternate exterior angles that are congruent,
  then the two lines are parallel.

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Identifying Parallel Lines

• Which lines are parallel if
  ?1 ? ?2? Justify your answer.
• Which lines are parallel if ?6 ? ?7? Justify
  your answer.

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Using Algebra

• What is the value of x for which a ll b?