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?
Proof: Alternate Interior Angles Theorem Given: l m Prove: 4 6
Other Angle Relationships Same-Side Interior Angles Theorem: If a transversal intersects two parallel lines, then same-side interior angles are supplementary.
Proof: Proving Angles Supplementary Given: a ll b Prove: 1 and 8 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
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?