Key Concept: Transversals and Angles Example 1: Classify Relationships Main Idea New Vocabulary NGSSS 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 Five-Minute Check 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
MA.8.G.2.2 Classify and determine the measure of angles, including angles created when parallel lines are cut by transversals. NGSSS
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 m4 = 40°, find m6 and m7. 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, m6 = 40. Since 6 and 7 are supplementary, the sum of their measures is 180°. m7 = 180° – 40° or 140° Example 3
Find an Angle Measure Answer: m6 = 40° and m7 = 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 m1 = 142°, find m8. 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, m5 + m4 = 125. Since m5 = 90°, m4 = 125 – 90 or 35°. Answer: m4 = 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
Classify 1 and 8 as alternate interior, alternate exterior, or corresponding angles. A. alternate interior B. alternate exterior C. corresponding Five Minute Check 1
Classify 2 and 7 as alternate interior, alternate exterior, or corresponding angles. A. alternate interior B. alternate exterior C. corresponding Five Minute Check 2
Classify 1 and 3 as alternate interior, alternate exterior, or corresponding angles. A. alternate interior B. alternate exterior C. corresponding Five Minute Check 3
Refer to the figure below. Line s is perpendicular to line t Refer to the figure below. Line s is perpendicular to line t. The measure of 1 is 35°. Find m2. A. 35° B. 55° C. 90° D. 145° Five Minute Check 4
Refer to the figure below. Line s is perpendicular to line t Refer to the figure below. Line s is perpendicular to line t. The measure of 1 is 35°. Find m3. A. 35° B. 55° C. 90° D. 145° Five Minute Check 5
A city planner is examining the intersections of three roads as shown below. Road X is parallel to Road Y. Find m2. A. 45° B. 135° C. 225° D. 315° Five Minute Check 6