1. Lesson 17 Angles Formed By Parallel Lines and a Transversal

2.  This lesson reviews three theorems dealing with angle measures that result from a transversal intersecting two parallel lines. (“Transversal” is the name given to a line that intersects parallel lines.)  In the diagram, the parallel lines are l and m; the transversal is k. l m k 1 2 3 4 5

3.  Theorem 1: Alternate interior angles are congruent. (For example, 2  3.)  Theorem 2: Corresponding angles are congruent. (For example, 1  3 and 2  5.)  Theorem 3: Interior angles on the same side of the transversal are supplementary. (For example, the sum of the measures of 4 and 2 equals 180

4. Example  In this figure, lines j and n are parallel and the line t is a transversal. Find the measure of m. tj n 100 xx yy

5.  Strategy: Start with an angle you know and use one of the theorems to find the missing angles.  Step 1: Which angle is known? An angle of 100 is shown in the diagram.  Step 2: Find the measure of x. x is a corresponding angle to the angle whose measure is 100. So the measure of x = 100 by Theorem 2.

6.  Step 3: Find the measure of y. Since y and x are vertical angles, x  y. (Remember, vertical angles are congruent.) Since the measure of x is 100. Then the measure of y is 100.

7. Solution  y = 100