Warm-Up Exercises

ANSWER D

2. What is the intersection of AD and DB?

1. Name a line that does not intersect AD.

ANSWER BC

Warm-Up ExercisesEXAMPLE 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?

Warm-Up ExercisesEXAMPLE 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.

Warm-Up ExercisesEXAMPLE 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.

Warm-Up ExercisesEXAMPLE 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

Warm-Up ExercisesGUIDED 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

Warm-Up ExercisesGUIDED 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.

Warm-Up ExercisesEXAMPLE 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.

d. ∠52and∠74and

Warm-Up ExercisesGUIDED PRACTICE for Example 3

Classify the pair of numbered angles.

ANSWER

corresponding angles

3.

Warm-Up ExercisesGUIDED PRACTICE for Example 3

Classify the pair of numbered angles.

4.

ANSWER

alternate exterior angles.

Warm-Up ExercisesGUIDED PRACTICE for Example 3

Classify the pair of numbered angles.

5.

ANSWER

alternate interior angles.

Warm-Up ExercisesDaily Homework 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

Warm-Up ExercisesDaily Homework Quiz

ANSWER Parallel

4. The figure shows a painting easel.

Does AB appear to be parallel,

perpendicular, or skew to CD?