3.1

Warm UpWarm Up

Lesson QuizLesson Quiz

Lesson PresentationLesson Presentation

Identify Pairs of Lines and Angles

3.1 Warm-Up

ANSWER D

2. What is the intersection of AD and DB?

1. Name a line that does not intersect AD.

ANSWER BC

3.1 Example 1

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

SOLUTION

AB , HG , and EF all appear parallel to CD , but only AB contains point A.

a.

3.1 Example 1

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?

SOLUTION

b. Line(s) skew to CD and containing point A

Both AG and AH appear skew to CD and contain point A.

b.

3.1 Example 1

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?

SOLUTION

c. BC, AD , DE , and FC all appear perpendicular to CD , but only AD contains point A.

c. Line(s) perpendicular to CD and containing point A

3.1 Example 1

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?

SOLUTION

d. Plane(s) parallel to plane EFG and containing point A

d. Plane ABC appears parallel to plane EFG and contains point A.

3.1 Example 2

Photography

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

Name a pair of parallel lines.

a.

SOLUTION

a. MD FE

3.1 Example 2

Photography

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

SOLUTION

Name a pair of perpendicular lines.

b.

b. MD BF

3.1 Example 2

Photography

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

SOLUTION

Is FE AC ? Explain.c.

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.

3.1 Guided Practice

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

ANSWER AH , EH

3.1 Guided Practice

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

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.

ANSWER

3.1 Example 3

SOLUTION

a. ∠51and∠62and∠73and∠84and

b. ∠72and∠54and

c. ∠81and∠63and

Identify all pairs of angles of the given type.

d. ∠52and∠74and

a. Corresponding

b. Alternate interior

c. Alternate exterior

Consecutive interiord.

3.1 Guided Practice

Classify the pair of numbered angles.

ANSWER

corresponding angles

3.

3.1 Guided Practice

Classify the pair of numbered angles.

4.

ANSWER

alternate exterior angles.

3.1 Guided Practice

Classify the pair of numbered angles.

5.

ANSWER

alternate interior angles.

3.1 Lesson Quiz

1. Name the pairs of corresponding angles .

2. Name the pairs of alternate interior angles .

3. Name the pairs of consecutive interior angles .

ANSWER 2 and 7; 3 and 6

ANSWER 2 and 3; 6 and 7

ANSWER 1 and 3; 5 and 7;

2 and 4; 6 and 8

3.1 Lesson Quiz

4. The figure shows a painting easel. Does AB appear to be parallel, perpendicular, or skew to CD?

ANSWER Parallel