Key Concept: Transversals and Angles Example 1: Classify Relationships Main Idea New Vocabulary Key Concept: Transversals and Angles Example 1: Classify Relationships Example 2: Classify Relationships Example 3: Find an Angle Measure Example 4: Find the Missing Measures Lesson Menu

Identify relationships of angles formed by two parallel lines cut by a transversal. Main Idea/Vocabulary

alternate interior angles alternate exterior angles perpendicular lines parallel lines transversal interior angles exterior angles alternate interior angles alternate exterior angles corresponding angles Main Idea/Vocabulary

Key Concept

Classify Relationships Classify 3 and 7 as alternate interior, alternate exterior, or corresponding angles. 3 and 7 are in the same position on the two lines. Answer: They are corresponding angles. Example 1

Classify 4 and 6 as alternate interior, alternate exterior, or corresponding angles. A. alternate interior B. alternate exterior C. corresponding Example 1 CYP

Classify Relationships Classify 2 and 8 as alternate interior, alternate exterior, or corresponding angles. 2 and 8 are interior angles that lie on opposite sides of the transversal. Answer: They are alternate interior angles. Example 2

Classify 1 and 5 as alternate interior, alternate exterior, or corresponding angles. A. alternate interior B. alternate exterior C. corresponding Example 2 CYP

Since 6 and 7 are supplementary, the sum of their measures is 180°. Find an Angle Measure GATES Mr. Adams installed the gate shown. Line c is parallel to line d. If m4 = 40°, find m6 and m7. Justify your answer. Since 4 and 6 are interior angles that lie on opposite sides of the transversal, they are alternate interior angles. Alternate interior angles are congruent. So, m6 = 40. Since 6 and 7 are supplementary, the sum of their measures is 180°. m7 = 180° – 40° or 140° Example 3

Find an Angle Measure Answer: m6 = 40° and m7 = 140° Example 3

GATES Use the gate shown. Line c is parallel to line d GATES Use the gate shown. Line c is parallel to line d. If m1 = 142°, find m8. A. 38° B. 42° C. 52° D. 142° Example 3 CYP

Find the Missing Measures In the figure, line a is parallel to line b, and line c is perpendicular to line d. The measure of 7 is 125°. What is the measure of 4? 7 and the sum of 5 and 4 are alternate exterior angles. So, m5 + m4 = 125. Since m5 = 90°, m4 = 125 – 90 or 35°. Answer: m4 = 35° Example 4

In the figure, line a is parallel to line b, and line c is perpendicular to line d. The measure of 8 is 43°. What is the measure of 1? A. 43° B. 45° C. 47° D. 90° Example 4 CYP