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3.1 Lines and Angles

3.1 Lines and Angles. Mr. Davenport Fall 2009. Objectives:. Objectives: Identify relationships between lines. Identify angles formed by transversals. Definitions. Parallel lines – Two lines are parallel lines if they are coplanar and do not intersect.

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3.1 Lines and Angles

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  1. 3.1 Lines and Angles Mr. Davenport Fall 2009

  2. Objectives: 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 5 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 2 4 1 6 8 3 5 7

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

  11. Assignment • P. 132 / 10-26, 32-36, 38, 41, 42, 47, 51, 61

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