7 2 Parallel and Perpendicular Lines Warm Up

7 -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. A part of a line between two points is called a segment ______. Course 3

7 -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. Course 3

7 -2 Parallel and Perpendicular Lines Learn to identify parallel and perpendicular lines and the angles formed by a transversal. Course 3

Parallel. Lesson and Perpendicular 7 -2 Insert Title Here. Lines Vocabulary parallel lines perpendicular lines transversal Course 3

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. Course 3

7 -2 Parallel and Perpendicular Lines The railroad ties are transversals to the tracks. The tracks 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. Course 3

7 -2 Parallel and Perpendicular Lines Caution! You cannot tell for certain if angles are congruent by measuring because measurement is not exact. Course 3

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°. 2, 4, 6, and 8 all measure 30°. Course 3

7 -2 Parallel and Perpendicular Lines Additional 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 @ 3 @ 5 @ 7 2 @ 4 @ 6 @ 8 Course 3 2 1 3 4 6 5 7 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 2 3 4 5 6 7 8 1, 4, 5, and 8 all measure 36°. 2, 3, 6, and 7 all measure 144°. Course 3

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 1 Course 3 2 3 4 5 6 7 8

7 -2 Parallel and Perpendicular Lines If two lines are intersected by a transversal and any of the angle pairs shown below are congruent, then the lines are parallel. This fact is used in the construction of parallel lines. Course 3

7 -2 Parallel and Perpendicular Lines PROPERTIES OF TRANSVERSALS TO PARALLEL LINES If two parallel lines are intersected by a transversal, • the acute angles that are formed are all congruent, • the obtuse angles are all congruent, • and any acute angle is supplementary to any obtuse angle. If the transversal is perpendicular to the parallel lines, all of the angles formed are congruent 90° angles. Course 3

7 -2 Parallel and Perpendicular Lines Writing Math The symbol for parallel is ||. The symbol for perpendicular is . Course 3

7 -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 All obtuse angles in the figure are congruent. m 4 = 124° Course 3

7 -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 the angle 124°. m 2 + 124° = 180° – 124° m 2 = 56° Course 3

7 -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 All acute angles in the figure are congruent. m 6 = 56° Course 3

7 -2 Parallel and Perpendicular Lines Check It Out: Example 2 A In the figure, line n || line m. Find the measure of the angle. 7 All obtuse angles in the figure are congruent m 7 = 144° Course 3 1 144° 3 4 5 6 7 8 m n

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

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

7 -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. If m 5 = 120° what is m 2? 60° Course 3