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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

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.

Identifying Congruent Angles

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

? If m?4 50, what is m?6?

Other Angle Relationships

- Same-Side Interior Angles Theorem If a

transversal intersects two parallel lines, then

same-side interior angles are supplementary.

Finding Measures of Angles

- What are the measures of each angle? Justify

each answer.

Finding an Angle Measure

- What is the value of y?

3-3 Proving Lines Parallel

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.

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.

Identifying Parallel Lines

- Which lines are parallel if

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

your answer.

Using Algebra

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