Parallel Lines and Planes

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Presentation transcript:

Parallel Lines and Planes 3-1

EXAMPLE 3 Identify angle relationships Identify all pairs of angles of the given type. a. Corresponding b. Alternate interior c. Alternate exterior Consecutive interior d. SOLUTION a. ∠ 5 1 and ∠ 6 2 ∠ 7 3 ∠ 8 4 b. ∠ 7 2 and ∠ 5 4 c. ∠ 8 1 and ∠ 6 3

EXAMPLE 3 Identify angle relationships d. ∠ 5 2 and ∠ 7 4

GUIDED PRACTICE for Example 3 Classify the pair of numbered angles. 3. ANSWER Angles are 1 and 5 corresponding angles.

GUIDED PRACTICE for Example 3 Classify the pair of numbered angles. 4. ANSWER Angles 2 and 7 are alternate exterior angles.

GUIDED PRACTICE for Example 3 Classify the pair of numbered angles. 5. ANSWER Angles 5 and 4 are alternate interior angles.

EXAMPLE 1 Identify relationships in space Think of each segment in the figure as part of a line. Which line(s) or plane(s) in the figure appear to fit the description? a. Line(s) parallel to CD and containing point A b. Line(s) skew to CD and containing point A c. Line(s) perpendicular to CD and containing point A d. Plane(s) parallel to plane EFG and containing point A

EXAMPLE 1 Identify relationships in space SOLUTION AB , HG , and EF all appear parallel to CD , but only AB contains point A. a. Both AG and AH appear skew to CD and contain point A. b. c. BC, AD , DE , and FC all appear perpendicular to CD , but only AD contains point A. d. Plane ABC appears parallel to plane EFG and contains point A.

GUIDED PRACTICE for Examples 1 and 2 1. Look at the diagram in Example 1. Name the lines through point H that appear skew to CD. ANSWER In the diagram the lines through the point H that appears skew to CD are AH and EH.

EXAMPLE 2 Identify parallel and perpendicular lines Photography The given line markings show how the roads are related to one another. Name a pair of parallel lines. a. Name a pair of perpendicular lines. b. Is FE AC ? Explain. c.

EXAMPLE 2 Identify parallel and perpendicular lines SOLUTION a. MD FE b. MD BF FE is not parallel to AC , because MD is parallel to FE and by the Parallel Postulate there is exactly one line parallel to FE through M. c.

GUIDED PRACTICE for Examples 1 and 2 2. In Example 2, can you use the Perpendicular Postulate to show that AC is not perpendicular to BF ? Explain why or why not. ANSWER Yes in Example 2 you can use the perpendicular postulate to show that AC is not perpendicular to BF. Since A is not on MD and MD is to BF, the perpendicular postulate guarantees that there is exactly one line through a point perpendicular to a line, so AC can not be perpendicular to BF also.

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