1. 3.1 Lines and Angles

2. Goal 1: Relationships Between Lines
Definitions:
Parallel lines - Two lines are parallel lines if they are coplanar and do not intersect.
Skew lines - Lines that do not intersect and are not coplanar.
Parallel planes - Two planes that do not intersect.

3. Example 1: Identifying Relationships in Space
Think of each segment in the diagram as part of a line. Which of the lines appear to fit the description?
Parallel to AB and contains D
Perpendicular to AB and contains D
Skew to AB and contains D
Name the plane(s) that contains D and appear to be parallel to plane ABE B C D A F G E H

4. Example 1: Identifying Relationships in Space (cont.)
a. Parallel to AB and contains D
CD, GH and EF are all parallel to AB, but only CD passes through D and is parallel to AB.
b. Perpendicular to AB and contains D
BC, AD, AE and BF are all perpendicular to AB, but only AD passes through D and is perpendicular to AB B C D A F G E H

5. Example 1: Identifying Relationships in Space (cont.)
c. Skew to AB and contains D
DG, DH, and DE all pass through D and are skew to AB.
d. Name the plane(s) that contains D and appear to be parallel to plane ABE
Only plane DCH contains D and is parallel to plane ABE B C D A F G E H

6. Postulate 13: 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. P l

7. Postulate 14: Perpendicular Postulate
If there is a line and a point not on the line, then there is exactly one line through the given point perpendicular to the given line. P l

8. Activity: A Perpendicular to a Line
Use the following steps to construct a line that passes through a given point P and is perpendicular to a given line l.
Place the compass at point P and draw an arc that intersects the line l twice. Label the intersections A and B.
Draw an arc with center A. Using the same radius, draw an arc with center B. Label the intersection of the arcs Q.
Use a straight edge to draw PQ. PQ  l.

9. Goal 2: Identifying Angles formed by Transversals
Angles 1 and 5 are corresponding angles
Angles 1 and 8 are alternate exterior angles
Angles 3 and 6 are alternate interior angles.
3 and 5 are consecutive interior angles
(also called same side interior angles)
Definitions:
Transversal: a line that intersects two or more coplanar lines at different points. 4 7 1 2 3 5 6 8

10. Example 2: Identifying Angle Relationships
List all pairs of angles
that fit the description.
a. Corresponding
1 and 5; 2 and 6; 3 and 7, 4 and 8
b. Alternate exterior
1 and 8, 2 and 7 2 4 1 6 8 3 5 7

11. Example 2: Identifying Angle Relationships (cont.)
List all pairs of angles
that fit the description.
c. Alternate interior
3 and 6, 4 and 5
d. Consecutive interior
3 and 5, 4 and 6 2 4 1 6 8 3 5 7