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3-2 Properties of Parallel Lines

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3-2 Properties of Parallel Lines Congruent Angle Relationships Corresponding Angles Postulate: If a transversal intersects two parallel lines, then corresponding ... – PowerPoint PPT presentation

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Title: 3-2 Properties of Parallel Lines


1
3-2 Properties of Parallel Lines
2
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.

3
Identifying Congruent Angles
  • Which angles measure 55?? How do you know?

4
? If m?4 50, what is m?6?
5
Other Angle Relationships
  • Same-Side Interior Angles Theorem If a
    transversal intersects two parallel lines, then
    same-side interior angles are supplementary.

6
Finding Measures of Angles
  • What are the measures of each angle? Justify
    each answer.

7
Finding an Angle Measure
  • What is the value of y?

8
3-3 Proving Lines Parallel
9
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.

10
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.

11
Identifying Parallel Lines
  • Which lines are parallel if
    ?1 ? ?2? Justify your answer.
  • Which lines are parallel if ?6 ? ?7? Justify
    your answer.

12
Using Algebra
  • What is the value of x for which a ll b?
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