1. 3.5 Using the Properties of Parallel lines Making Lines Parallel

2. Theorem used to use the idea of parallel lines If two lines are parallel to the same line, then they are parallel to each other. If a // b and b // c, then a // c.

3. If you were hanging wallpaper. To make sure the pattern is going to up and down and not at an angle; you need parallel lines. With a plumb line, find a vertical line. defined (plumb line n. 1. A line from which a weight is suspended to determine verticality or depth. 2. A line regarded as directed exactly toward the earth's center of gravity.

4. If you were hanging wallpaper. To make sure the pattern is going to up and down and not at an angle; you need parallel lines. With a plumb line, find a vertical line. defined (plumb line n. 1. A line from which a weight is suspended to determine verticality or depth. 2. A line regarded as directed exactly toward the earth's center of gravity.

5. Plumb line can be made with a piece of string and metal washer. With a pencil mark the line made by the line. Place the edge of your first piece of wallpaper on the line.

6. Plumb line can be made with a piece of string and metal washer. With a pencil mark the line made by the line. Place the edge of your first piece of wallpaper on the line.

7. Plumb line can be made with a piece of string and metal washer. With a pencil mark the line made by the line. Place the edge of your first piece of wallpaper on the line. Use the edge of the wallpaper for the next edge.

8. How do you know the edge are parallel? With a pencil mark the line made by the line. Place the edge of your first piece of wallpaper on the line. Use the edge of the wallpaper for the next edge.

9. How do you know the edge are parallel? If two lines are parallel to the same line, then they are parallel to each other. All the edges will be parallel.

10. Another Theorem In a plane, if 2 lines are perpendicular to a third line, then they are parallel to each other. If r v and r q, then v // q

11. Lets prove it #1. r v and r q#1. Given #2. #2.All right angle congruent #3. v // q#3. If two cut by a transversal and Correspond angles are congruent then the lines are parallel

12. Lets prove it #1. r v and r q#1. Given #2. #2.All right angle congruent #3. v // q#3. If two cut by a transversal and Correspond angles are congruent then the lines are parallel

13. Lets prove it #1. r v and r q#1. Given #2. #2.All right angle congruent #3. v // q#3. If two cut by a transversal and Correspond angles are congruent then the lines are parallel

14. Lets prove it #1. r v and r q#1. Given #2. #2.All right angle congruent #3. v // q#3. If two cut by a transversal and Correspond angles are congruent then the lines are parallel

15. Lets prove it #1. r v and r q#1. Given #2. #2.All right angle congruent #3. v // q#3. If two cut by a transversal and Correspond angles are congruent then the lines are parallel

16. Homework Page 160 – 163 #8 – 13, 15 – 23 odd 31, 33- 36, 43- 47 odd, 50