3.1 Lines and Angles

1. 3.1 Lines and Angles

2. Standard/Objectives: Standard 3: Students will have a foundation in geometric concepts. Objectives: • Identify relationships between lines. • Identify angles formed by transversals.

3. 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.

4. Think of each segment in the diagram. Which 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 Example 1: Identifying relationships in space B C D A F G E H

5. Solution • CD, GH and EF are all parallel to AB, but only CD passes through D and is parallel to AB. • BC, AD, AE and BF are all perpendicular to AB, but only AD passes through D and is perpendicular to AB • DG, DH, and DE all pass through D and are skew to AB. • Only plane DCH contains D and is parallel to plane ABE

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. Transversal: a line that intersects two or more coplanar lines at different points. 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 1 2 3 4 5 6 7 8 Definitions:

9. List all pairs of angles that fit the description. Corresponding Alternate exterior Alternate interior Consecutive interior Example 2: Identifying Angle relationships 8 7 1 6 5 2 3 4

10. Solution: • 1 and 3; 2 and 4; 5 and 7, 6 and 8 • 4 and 8, 1 and 5 • 3 and 7, 2 and 6 • 7 and 6, 2 and 3