1. 7-2 Parallel and Perpendicular Lines Warm Up Complete each sentence. 1. Angles whose measures have a sum of 90° are _______________. 2. Vertical angles have equal measures, so they are ______________. 3. Angles whose measures have a sum of 180° are ______________. 4. An angle that measures less than 90° is a(n) ____________ angle. complementary congruent supplementary acute

2. 7-2 Parallel and Perpendicular Lines Learn to identify parallel and perpendicular lines and the angles formed by a transversal.

3. 7-2 Parallel and Perpendicular Lines Vocabulary parallel lines perpendicular lines transversal

4. 7-2 Parallel and Perpendicular Lines Parallel lines are lines in a plane that never meet, like a set of perfectly straight, infinite train tracks. Perpendicular lines are lines that intersect at 90° angles.

5. 7-2 Parallel and Perpendicular Lines You cannot tell if angles are congruent by measuring because measurement is not exact. Caution!

6. 7-2 Parallel and Perpendicular Lines Additional Example 1: Identifying Congruent Angles Formed by a Transversal Measure the angles formed by the transversal and parallel lines. Which angles seem to be congruent? 1, 3, 5, and 7 all measure 150° and appear to be congruent. 2, 4, 6, and 8 all measure 30° and appear to be congruent.

7. 7-2 Parallel and Perpendicular Lines Additional Example 1 Continued Angles circled in blue appear to be congruent to each other, and angles circled in red appear to be congruent to each other. 1  3 5  7 2  4  6  8

8. 7-2 Parallel and Perpendicular Lines Check It Out: Example 1 Measure the angles formed by the transversal and parallel lines. Which angles seem to be congruent? 1, 4, 5, and 8 all measure 36° and appear to be congruent. 2, 3, 6, and 7 all measure 144° and appear to be congruent. 1 2 3 4 5 6 7 8

9. 7-2 Parallel and Perpendicular Lines Check It Out: Example 1 Continued Angles marked in blue appear to be congruent to each other, and angles marked in red appear to be congruent to each other. 1  4 5  8 2  3  6  7 2 3 6 7 1 4 5 8

10. 7-2 Parallel and Perpendicular Lines Some pairs of the eight angles formed by two parallel lines and a transversal have special names.

11. 7-2 Parallel and Perpendicular Lines

12. 7-2 Parallel and Perpendicular Lines The symbol for parallel is ||. The symbol for perpendicular is . Writing Math

13. 7-2 Parallel and Perpendicular Lines In the figure, line l || line m. Find the measure of the angle. Additional Example 2A: Finding Angle Measures of Parallel Lines Cut by Transversals 44 m  4 = 124° The 124 angle and 4 are corresponding angles.

14. 7-2 Parallel and Perpendicular Lines Additional Example 2B: Finding Angle Measures of Parallel Lines Cut by Transversals Continued 22 m2 + 124° = 180° 2 is supplementary to angle 124°. m2 = 56° –124° In the figure, line l || line m. Find the measure of the angle.

15. 7-2 Parallel and Perpendicular Lines Additional Example 2C: Finding Angle Measures of Parallel Lines Cut by Transversals Continued 66 m  6 = 56° In the figure, line l || line m. Find the measure of the angle. m6 + 124° = 180° 6 is supplementary to angle 6. m6 = 56° –124°

16. 7-2 Parallel and Perpendicular Lines In the figure, line n || line m. Find the measure of the angle. Check It Out: Example 2A 77 m  7 = 144° The 144 angle and 7 are alternate exterior angles. 1 144° 3 4 5 6 7 8 m n

17. 7-2 Parallel and Perpendicular Lines 11 m1 + 144° = 180° 1 is supplementary to the 144° angle. m1 = 36° –144° 1 144° 3 4 5 6 7 8 m n In the figure, line n || line m. Find the measure of the angle. Check It Out: Example 2B

18. 7-2 Parallel and Perpendicular Lines 5 and 1 are corresponding angles. 55 m  5 = 36° 1 144° 3 4 5 6 7 8 m n In the figure, line n || line m. Find the measure of the angle. Check It Out: Example 2C

19. 7-2 Parallel and Perpendicular Lines Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

20. 7-2 Parallel and Perpendicular Lines Lesson Quiz In the figure, a || b. 1. Name the angles congruent to 3. 2. Name all the angles supplementary to 6. 3. If m1 = 105° what is m3? 4. What is m6? 1, 5, 7 1, 3, 5, 7 105° 75°

21. 7-2 Parallel and Perpendicular Lines 1. In the figure, x || y. Identify the angles congruent to 3. A. 1, 2, 4 B. 2, 4, 6 C. 4, 5, 6 D. 1, 5, 8 Lesson Quiz for Student Response Systems

22. 7-2 Parallel and Perpendicular Lines 2. In the figure, x || y. If m5 = 115°, what is m7? A. 25° B. 65° C. 75° D. 115° Lesson Quiz for Student Response Systems