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Warm Up

Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. complementary. Warm Up Complete each sentence. 1. Angles whose measures have a sum of 90° are _______________ . 2. Vertical angles have equal measures, so they are ______________.

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Warm Up

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. complementary 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. supplementary acute congruent

  3. I can identify parallel and perpendicular lines and the angles formed by a transversal.

  4. Vocabulary parallel lines perpendicular lines transversal

  5. 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.

  6. The sides of the windows are transversals to the top and bottom. The top and bottom of the windows are parallel. 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.

  7. 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?

  8. 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

  9. Check It Out: Example 1 Measure the angles formed by the transversal and parallel lines. Which angles seem to be congruent? 1 2 4 3 5 6 8 7

  10. 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 1 3 4 6 5 7 8

  11. Some pairs of the eight angles formed by two parallel lines and a transversal have special names.

  12. Writing Math The symbol for parallel is ||. The symbol for perpendicular is .

  13. Additional Example 2A: Finding Angle Measures of Parallel Lines Cut by Transversals In the figure, line l|| line m. Find the measure of all angles.

  14. Additional Example 2B: Finding Angle Measures of Parallel Lines Cut by Transversals Continued In the figure, line l || line m. Find the measure of the angle.

  15. 144° 1 m 4 3 6 5 n 8 7 Check It Out: Example 2A In the figure, line n || line m. Find the measure of the angle. The 144 angle and 7 are alternate exterior angles. 7 m7 = 144°

  16. 144° 1 m 4 3 6 5 n 8 7 Check It Out: Example 2B In the figure, line n || line m. Find the measure of the angle. 1 is supplementary to the 144° angle. m1 = 36°

  17. 144° 1 m 4 3 6 5 n 8 7 Check It Out: Example 2C In the figure, line n || line m. Find the measure of the angle. 5 and 1 are corresponding angles. 5 m5 = 36°

  18. Assignment Bookwork Pg. 204-205 All problems 1-26 Due at end of tomorrow’s class

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

  20. Lesson Quiz for Student Response Systems 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

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

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