1. Section 3.1: Lines and Angles

2. Goals Identify relationships between lines
Identify angles formed by transversals

3. Relationships Between Lines
Parallel Lines
Coplanar lines that do not intersect
Skew Lines
Lines that do not intersect and are not coplanar
Parallel Planes
Planes that do not intersect
Do example 1 on page 129

4. Examples of Skew Lines

5. Parallel Postulate
If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line l P

6. Perpendicular Postulate
If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line l P

7. Identifying Angles Formed by Transversals
A line that intersects 2 or more coplanar lines at different points
Usually the transversal is named t

8. Angles formed by transversals1 t 2 3 4 5 6 7 8
Corresponding Angles
2 angles that occupy corresponding positions
Angles 1 and 5 are corresponding angles

9. Angles formed by transversals1 t 2 3 4 5 6 7 8
Alternate Exterior Angles
2 angles that lie outside the two lines on opposite sides of the transversal
Angles 1 and 8 are alternate exterior angles

10. Angles formed by transversals1 t 2 3 4 5 6 7 8
Alternate Interior Angles
2 angles that lie between the 2 lines on opposite sides of the transversal
Angles 3 and 6 are alternate interior angles

11. Angles formed by transversals1 t 2 3 4 5 6 7 8
Consecutive Interior Angles
2 angles that lie between the 2 lines on the same side of the transversal
Angles 3 and 5 are consecutive interior angles (Consecutive interior angles are also called same side interior angles.)