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Warm Up

Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. 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. 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. 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. Sunshine State Standards MA.8.G.2.2 Classify and determine the measure of angles, including angles created when parallel lines are cut by transversals.

  5. Vocabulary parallel lines perpendicular lines transversal

  6. Parallel lines are lines in a plane that never meet. Perpendicular lines are lines that intersect at 90° angles.

  7. 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.

  8. Caution! You cannot tell if angles are congruent by measuring because measurement is not exact.

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

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

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

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

  15. –124° –124° 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. 2 2 is supplementary to angle 124°. m2 + 124° = 180° m2 = 56°

  16. –124° –124° Additional Example 2C: Finding Angle Measures of Parallel Lines Cut by Transversals Continued In the figure, line l || line m. Find the measure of the angle. 6 6 is supplementary to angle 6. m6 + 124° = 180° m6 = 56° m6 = 56°

  17. 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 each angle. Justify your answer. 5 36°; possible answer: 5 is congruent to 1, which is supplementary to the given angle,180° – 144° = 36°

  18. 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 each angle. Justify your answer. 7 144°; possible answer: 7 and the 144° angle are alternate exterior angles, which are congruent.

  19. 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 each angle. Justify your answer. 8 36°; possible answer: 8 and 7 are supplementary angles, 180° – 144° = 36°

  20. 144° 1 m 4 3 6 5 n 8 7 Check It Out: Example 2D In the figure, line n || line m. Find the measure of each angle. Justify your answer. 6 144°; possible answer: 6 and the 144° angle are corresponding angles, which are congruent.

  21. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  22. 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°

  23. 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

  24. 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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