1. 4.5 Introduction to Parallel Lines
Objectives:
Recognize planes
Recognize transversals and angle pairs
Recognize parallel lines

2. Plane: extends in two directions, usually represented by a shape that looks like a tabletop or wall.
Plane M or plane ABC D C B A M
Coplanar: any objects, lines, points, etc., that lie in the same plane.
Noncoplanar: any objects, lines, points, etc., that do not lie in the same plane.

3. Transversal: a line that intersects two coplanar lines but not concurrently.

4. interior
exterior

5. Corresponding angles: angles on the same side of the transversal, but one is in the interior and the other in the exterior. 2 2 1 1 4 4 3 3 5 5 6 6 8 8 7 7

6. Alternate interior angles: angles on opposite sides of the transversal and in the interior.2 1 4 4 3 3 5 5 6 6 8 7

7. Alternate exterior angles: angles on opposite sides of the transversal and in the exterior.2 2 1 1 4 3 5 6 8 8 7 7

8. Same side interior angles: angles on the same side of the transversal and in the interior.2 1 3 3 4 4 5 5 6 6 8 7

9. Same side exterior angles: angles on the same side of the transversal and in the exterior.2 2 1 1 4 3 5 6 8 8 7 7

10. 1 5 4 2 6 8 7 3 Example 1: Find: a) All corresponding angles
b) All same side interior angles
c) All alternate exterior angles
d) All alternate interior angles
e) All same side exterior angles 1 2 4 3 5 6 8 7

11. Example 2: Find:
a) All corresponding angles
b) All same side interior angles
c) All alternate exterior angles
d) All alternate interior angles
e) All same side exterior angles 1 3 4 5 2 6 8 7 l1 l2 l3 9 12 11 10

12. A transversal must be a side in each angle!
Example 3: Name the numbered angles: 1 2 3 4 1 2 5 6 3 4
A transversal must be a side in each angle!

13. Example 4: Name some angles:B F E D C

14. Parallel lines: Two coplanar lines that do not intersect.B D