9 2 Parallel and Perpendicular Lines Warm Up

9 -2 Parallel and Perpendicular Lines Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

9 -2 Parallel and Perpendicular Lines Warm Up Complete each sentence. 1. Angles whose measures have a sum of 90° are ________. complementary 2. Vertical angles have equal measures, so they are congruent _______. 3. Angles whose measures have a sum of 180° are supplementary _______. 4. An angle that measures less than 90° is a(n) acute ______ angle.

9 -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.

9 -2 Parallel and Perpendicular Lines 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.

9 -2 Parallel and Perpendicular Lines Vocabulary parallel lines perpendicular lines transversal

9 -2 Parallel and Perpendicular Lines Parallel lines are lines in a plane that never meet. Perpendicular lines are lines that intersect at 90° angles.

9 -2 Parallel and Perpendicular Lines The sides of the windows are transversals to the top and bottom. The top and bottom of the windows are paralle 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.

9 -2 Parallel and Perpendicular Lines Caution! You cannot tell if angles are congruent by measuring because measurement is not exact.

9 -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.

9 -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

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

9 -2 Parallel and Perpendicular Lines Some pairs of the eight angles formed by two parallel lines and a transversal have special names.

9 -2 Parallel and Perpendicular Lines

9 -2 Parallel and Perpendicular Lines Writing Math The symbol for parallel is ||. The symbol for perpendicular is .

9 -2 Parallel and Perpendicular Lines Additional Example 2 A: Finding Angle Measures of Parallel Lines Cut by Transversals In the figure, line l || line m. Find the measure of the angle. 4 The 124 angle and 4 are corresponding angles. m 4 = 124°

9 -2 Parallel and Perpendicular Lines Additional Example 2 B: 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° – 124° m 2 = 56°

9 -2 Parallel and Perpendicular Lines Additional Example 2 C: 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° – 124° m 6 = 56°

9 -2 Parallel and Perpendicular Lines Check It Out: Example 2 A In the figure, line n || line m. Find the measure of each angle. Justify your answer. 1 144° m 5 3 4 5 6 n 7 8 36°; possible answer: 5 is congruent to 1, which is supplementary to the given angle, 180° – 144° = 36°

9 -2 Parallel and Perpendicular Lines Check It Out: Example 2 B In the figure, line n || line m. Find the measure of each angle. Justify your answer. 1 144° 7 3 4 5 6 7 8 m n 144°; possible answer: 7 and the 144° angle are alternate exterior angles, which are congruent.

9 -2 Parallel and Perpendicular Lines Check It Out: Example 2 C In the figure, line n || line m. Find the measure of each angle. Justify your answer. 1 144° 8 3 4 5 6 7 8 m n 36°; possible answer: 8 and 7 are supplementary angles, 180° – 144° = 36°

9 -2 Parallel and Perpendicular Lines Check It Out: Example 2 D In the figure, line n || line m. Find the measure of each angle. Justify your answer. 1 144° 6 3 4 5 6 7 8 m n 144°; possible answer: 6 and the 144° angle are corresponding angles, which are congruent.

9 -2 Parallel and Perpendicular Lines Lesson Quizzes Standard Lesson Quiz for Student Response Systems

9 -2 Parallel and Perpendicular Lines 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°

9 -2 Parallel and Perpendicular Lines 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

9 -2 Parallel and Perpendicular Lines 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°