1. Warm Up #2 (3/12/09) 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. Lines in a plane that never intersect are ___________. Course 3 7-2 Parallel and Perpendicular Lines complementary congruent supplementary parallel

2. M8G1. Students will understand and apply the properties of parallel and perpendicular lines and understand the meaning of congruence. a. Investigate characteristics of parallel and perpendicular lines both algebraically and geometrically. b. Apply properties of angle pairs formed by parallel lines cut by a transversal. d. Understand the meaning of congruence: that all corresponding angles are congruent and all corresponding sides are congruent.

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

4. 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.

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

6. 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 1 3 5 7 2 4 6 8

7. 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 2 3 6 7 1 4 5 8

8. Course 3 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.

9. 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.

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

11. In the figure, line l || line m. Find the measure of the angle. Course 3 7-2 Parallel and Perpendicular Lines Additional Example 2A: Finding Angle Measures of Parallel Lines Cut by Transversals 44 m  4 = 124° All obtuse angles in the figure are congruent.

12. Course 3 7-2 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 the angle 124°. m2 = 56° –124° In the figure, line l || line m. Find the measure of the angle.

13. Course 3 7-2 Parallel and Perpendicular Lines Additional Example 2C: Finding Angle Measures of Parallel Lines Cut by Transversals Continued All acute angles in the figure are congruent. 66 m  6 = 56° In the figure, line l || line m. Find the measure of the angle.

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

15. Course 3 7-2 Parallel and Perpendicular Lines 55 m5 + 144° = 180° 5 is supplementary to the angle 144°. m5 = 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

16. Course 3 7-2 Parallel and Perpendicular Lines All acute angles in the figure are congruent 11 m  1 = 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

17. Course 3 7-2 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. If m5 = 120° what is m2? 1, 5, 7 1, 3, 5, 7 105° 60°