Chapter 3.2 Notes: Use Parallel Lines and Transversals Goal: You will use angles formed by parallel lines and transversals.

Postulate 15 Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Ex.1: The measure of three of the numbered angles is 120o. Identify the angles. Explain your reasoning.

Theorem 3.1 Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Theorem 3.2 Alternate Exterior Angles Theorem: If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. Theorem 3.3 Consecutive Interior Angles Thm: If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

Ex.2: Find the value of x.

Ex.3: Find the value of x.

Ex. 4: Use the diagram below. a Ex.4: Use the diagram below. a. If , find and Tell which postulate or theorem you used in each case. b. If and , what is the value of x? Show your steps.

Ex.5: Find the value of x and y. Ex.6: Find and

Ex.7: Find the

Ex.8: Find the value of x.