Parallel Lines and Parallel Lines and PlanesPlanes

Parallel Lines and Parallel Lines and PlanesPlanes

3-13-1

EXAMPLE 3 Identify angle relationships

a. Corresponding

b. Alternate interior

c. Alternate exterior

Consecutive interiord.

SOLUTION

a. ∠51and∠62and∠73and∠84and

b. ∠72and∠54and

c. ∠81and∠63and

Identify all pairs of angles of the given type.

EXAMPLE 3

d. ∠52and∠74and

Identify angle relationships

GUIDED PRACTICE for Example 3

Classify the pair of numbered angles.

ANSWER

Angles are 1 and 5 corresponding angles.

3.

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

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.

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

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

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.