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Parallel Lines and Planes

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Parallel Lines and Planes

3-1

Identify all pairs of angles of the given type.

b.

a.

Corresponding

Alternate interior

d.

Consecutive interior

Alternate exterior

c.

and

and

and

and

and

and

and

and

∠ 8

∠ 7

∠ 6

∠ 5

∠ 5

∠ 8

∠ 6

∠ 7

2

3

4

1

3

4

1

2

a.

b.

c.

EXAMPLE 3

Identify angle relationships

SOLUTION

d.

and

and

∠ 5

∠ 7

2

4

EXAMPLE 3

Identify angle relationships

3.

ANSWER

Angles are 1 and 5 corresponding angles.

for Example 3

GUIDED PRACTICE

Classify the pair of numbered angles.

4.

ANSWER

Angles 2 and 7 are alternate exterior angles.

for Example 3

GUIDED PRACTICE

Classify the pair of numbered angles.

5.

ANSWER

Angles 5 and 4 are alternate interiorangles.

for Example 3

GUIDED PRACTICE

Classify the pair of numbered angles.

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 CDand containing point A

b.

Line(s) skew to CDand containing point A

Line(s) perpendicular to CDand containing point A

c.

d.

Plane(s) parallel to plane EFGand containing point A

EXAMPLE 1

Identify relationships in space

AB, HG, and EFall appear parallel to CD, but only ABcontains point A.

a.

b.

Both AGand AHappear skew to CDand contain point A.

BC, AD, DE, and FCall appear perpendicular to CD, but only ADcontains pointA.

c.

PlaneABCappears parallel to plane EFGand contains point A.

d.

EXAMPLE 1

Identify relationships in space

SOLUTION

1.

Look at the diagram in Example 1. Name the lines through point Hthat appear skew to CD.

ANSWER

In the diagram the lines through the point H that

appears skew to CD are AH and EH.

for Examples 1 and 2

GUIDED PRACTICE

Photography

The given line markings show how the roads are related to one another.

a.

Name a pair of parallel lines.

b.

Name a pair of perpendicular lines.

Is FEAC? Explain.

c.

EXAMPLE 2

Identify parallel and perpendicular lines

b.

MDBF

c.

FEis not parallel to AC, because MDis parallel to FEand by the Parallel Postulate there is exactly one line parallel to FEthrough M.

a.

MDFE

EXAMPLE 2

Identify parallel and perpendicular lines

SOLUTION

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.

for Examples 1 and 2

GUIDED PRACTICE

2.

In Example 2, can you use the Perpendicular Postulate to show that ACis not perpendicular to BF? Explain why or why not.