Warm-Up

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Warm-Up

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Section 3.3 Proving Lines are Parallel

• SWBAT prove that two lines are parallel

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Review

• Yesterday we learned that if two parallel lines
  are cut by a transversal then.
• Corresponding angles are congruent
• Alternate exterior angles are congruent
• Alternate exterior angles are congruent
• Consecutive interior angles are supplementary
• Today we will use the converse of these
  statements to prove that lines are parallel.

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Corresponding Angles Converse

• If two lines are cut by a transversal so that
  corresponding angles are congruent, then the
  lines are parallel

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Example

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Alternate Interior Angles Converse

• If two lines are cut by a transversal so that
  alternate interior angles are congruent then the
  lines are parallel

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Alternate Exterior Angles Converse

• If two lines are cut by a transversal so that
  alternate exterior angles are congruent, then the
  lines are parallel.

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Example

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Consecutive (same side) Interior Angles Converse

• If two lines are cut by a transversal so that
  consecutive (same side) interior angles are
  supplementary, then the lines are parallel

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Example

• Are the lines parallel? How could you prove this
  from the information given?

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Example

• Are the lines parallel? How could you prove this
  from the information given?

12
Example

• Are the lines parallel? How could you prove this
  from the information given?

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Example

• Find the values of x that make r s