1. 5-2 Parallel and Perpendicular Lines Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 5-2 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

3. 5-2 Parallel and Perpendicular Lines Problem of the Day The square root of 1,813,141,561 is a whole number. Is it odd or even? How do you know? Odd: An odd number can only be the product of two odd numbers.

4. 5-2 Parallel and Perpendicular Lines Learn to identify parallel and perpendicular lines and the angles formed by a transversal.

5. 5-2 Parallel and Perpendicular Lines Vocabulary parallel lines perpendicular lines transversal

6. 5-2 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.

7. 5-2 Parallel and Perpendicular Lines The sides of the windows are transversals to the top and bottom. A transversal is a line that intersects two or more lines that lie in the same plane. Transversals to parallel lines form angles with special properties. The top and bottom of the windows are parallel.

8. 5-2 Parallel and Perpendicular Lines You cannot tell if angles are congruent by measuring because measurement is not exact. Caution!

9. 5-2 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.

10. 5-2 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

11. 5-2 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

12. 5-2 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

13. 5-2 Parallel and Perpendicular Lines Some pairs of the eight angles formed by two parallel lines and a transversal have special names.

14. 5-2 Parallel and Perpendicular Lines

15. 5-2 Parallel and Perpendicular Lines The symbol for parallel is ||. The symbol for perpendicular is . Writing Math

16. 5-2 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.

17. 5-2 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.

18. 5-2 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°

19. 5-2 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

20. 5-2 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

21. 5-2 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

22. 5-2 Parallel and Perpendicular Lines Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

23. 5-2 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°

24. 5-2 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

25. 5-2 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