Definitions Parallel lines: Two lines are parallel lines if and only if they do not intersect and are coplanar. Skew Lines: Two lines are skew lines if.

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Presentation transcript:

Definitions Parallel lines: Two lines are parallel lines if and only if they do not intersect and are coplanar. Skew Lines: Two lines are skew lines if and only if they do not intersect and are not coplanar. Parallel Planes: Two planes are parallel if and only if they do not intersect.

EXAMPLE 1 Identify relationships in space d. Plane ( s ) parallel to plane EFG and containing point A c. Line ( s ) perpendicular to CD and containing point A a. Line ( s ) parallel to CD and containing point A b. Line ( s ) skew to CD and containing point A 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?

EXAMPLE 1 SOLUTION Identify relationships in space 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. d. Plane ABC appears parallel to plane EFG and contains point A. c. BC, AD, DE, and FC all appear perpendicular to CD, but only AD contains point A.

Postulates

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

EXAMPLE 2 b. MD BF Identify parallel and perpendicular lines 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. SOLUTION a. MD FE

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 AH, EH

Definitions

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; 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.

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

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