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. 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.

1 105om 4, 5m m 8.m

3 68om 8 (2 4)om x

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

Ex.6: Find and 1m 2m

Ex.8: Find the value of x.