Problem 1

Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles.

$$

\angle 2 \text { and } \angle 6

$$

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Problem 2

Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles.

$$

\angle 8 \text { and } \angle 6

$$

Daniel P.

Numerade Educator

Problem 3

Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles.

$$

\angle 2 \text { and } \angle 3

$$

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Problem 4

Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles.

$$

\angle 3 \text { and } \angle 7

$$

Daniel P.

Numerade Educator

Problem 5

Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles.

$$

\angle 5 \text { and } \angle 7

$$

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Problem 6

Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles.

$$

\angle 3 \text { and } \angle 1

$$

Daniel P.

Numerade Educator

Problem 7

Name the two lines and the transversal that form each pair of angles.

$$

\angle 2 \text { and } \angle 3

$$

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Problem 8

Name the two lines and the transversal that form each pair of angles.

$$

\angle 1 \text { and } \angle 4

$$

Daniel P.

Numerade Educator

Problem 9

Name the two lines and the transversal that form each pair of angles.

$$

\angle P \text { and } \angle P S R

$$

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Problem 10

Name the two lines and the transversal that form each pair of angles.

$$

\angle 5 \text { and } \angle P S R

$$

Daniel P.

Numerade Educator

Problem 11

Name the two lines and the transversal that form each pair of angles.

$$

\angle 5 \text { and } \angle P Q R

$$

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Problem 12

Classify each pair of angles as alternate interior, same-side interior, or corresponding angles.

$$

\angle E B A \text { and } \angle F C B

$$

Daniel P.

Numerade Educator

Problem 13

Classify each pair of angles as alternate interior, same-side interior, or corresponding angles.

$$

\angle D C H \text { and } \angle C B J

$$

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Problem 14

Classify each pair of angles as alternate interior, same-side interior, or corresponding angles.

$$

\angle F C B \text { and } \angle C B L

$$

Daniel P.

Numerade Educator

Problem 15

Classify each pair of angles as alternate interior, same-side interior, or corresponding angles.

$$

\angle F C L \text { and } \angle B L C

$$

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Problem 16

Classify each pair of angles as alternate interior, same-side interior, or corresponding angles.

$$

\angle H C B \text { and } \angle C B J

$$

Daniel P.

Numerade Educator

Problem 17

Classify each pair of angles as alternate interior, same-side interior, or corresponding angles.

$$

\angle G C H \text { and } \angle G L J

$$

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Problem 18

In Exercises $18-20$ use two lines of notebook paper as parallel lines and draw any transversal. Use a protractor to measure.

Measure one pair of corresponding angles. Repeat the experiment with another transversal. What appears to be true?

Daniel P.

Numerade Educator

Problem 19

In Exercises $18-20$ use two lines of notebook paper as parallel lines and draw any transversal. Use a protractor to measure.

Measure one pair of alternate interior angles. Repeat the experiment with another transversal. What appears to be true?

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Problem 20

In Exercises $18-20$ use two lines of notebook paper as parallel lines and draw any transversal. Use a protractor to measure.

Measure one pair of same-side interior angles. Repeat the experiment with another transversal. What appears to be true?

Daniel P.

Numerade Educator

Problem 21

Draw a large diagram showing three transversals intersecting two nonparallel lines $l$ and $n .$ Number three pairs of same side interior angles on the same sides of the transversals, as shown in the diagram.

a. Find $m \angle 1+m \angle 2$

b. Find $m \angle 3+m \angle 4$

c. Predict the value of $m \angle 5+m \angle 6 .$ Then check your prediction by measuring.

d. What do you conclude?

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Problem 22

Draw a diagram of a six-sided box by following the steps below.

Draw a six-sided top. Then draw an exact copy of the top directly below it.

Draw vertical edges. Make invisible edges dashed.

Daniel P.

Numerade Educator

Problem 23

Exercises $23-29$ refer to the diagram in Step 2 of Exercise $22 .$

Name five lines that appear to be parallel to $\overline{A G}$ .

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Problem 24

Exercises $23-29$ refer to the diagram in Step 2 of Exercise $22 .$

Name three lines that appear to be parallel to $\overline{A B}$ .

Daniel P.

Numerade Educator

Problem 25

Exercises $23-29$ refer to the diagram in Step 2 of Exercise $22 .$

Name four lines that appear to be skew to $\overline{A B}$ .

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Problem 26

Exercises $23-29$ refer to the diagram in Step 2 of Exercise $22 .$

Name two planes parallel to $\overrightarrow{A F}$ .

Daniel P.

Numerade Educator

Problem 27

Exercises $23-29$ refer to the diagram in Step 2 of Exercise $22 .$

Name four planes parallel to $\overrightarrow{F L}$ .

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Problem 28

Exercises $23-29$ refer to the diagram in Step 2 of Exercise $22 .$

How many pairs of parallel planes are shown?

Daniel P.

Numerade Educator

Problem 29

Exercises $23-29$ refer to the diagram in Step 2 of Exercise $22 .$

Suppose the top and bottom of the box lie in parallel planes.

Explain how Theorem $3-1$ can be used to prove $\overline{C D} \| \frac{\text { planes. }}{I J}$ .

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Problem 30

Complete each statement with the word always, sometimes, or never.

When there is a transversal of two lines, the three lines are ___ coplanar.

Daniel P.

Numerade Educator

Problem 31

Complete each statement with the word always, sometimes, or never.

Three lines intersecting in one point are _____ coplanar.

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Problem 32

Complete each statement with the word always, sometimes, or never.

Two lines that are not coplanar _____ intersect.

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Problem 33

Complete each statement with the word always, sometimes, or never.

Two lines parallel to a third line are _____ parallel to each other.

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Problem 34

Complete each statement with the word always, sometimes, or never.

Two lines skew to a third line are ______ skew to each other.

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Problem 35

Complete each statement with the word always, sometimes, or never.

Two lines perpendicular to a third line are _____ perpendicular to each other.

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Problem 36

Complete each statement with the word always, sometimes, or never.

Two planes parallel to the same line are _____ parallel to each other.

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Problem 37

Complete each statement with the word always, sometimes, or never.

Two planes parallel to the same plane are _____ parallel to each other.

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Problem 38

Complete each statement with the word always, sometimes, or never.

Lines in two parallel planes are _____ perpendicular to each other.

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Problem 39

Complete each statement with the word always, sometimes, or never.

Two lines parallel to the same plane are _____ parallel to each other.

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Problem 40

Draw each figure described.

Lines $a$ and $b$ are skew. lines $b$ and $c$ are skew. and $a \| c$

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Problem 41

Draw each figure described.

Lines $d$ and $e$ are skew. lines $e$ and $f$ are skew. and $d \perp f$

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Problem 42

Draw each figure described.

Line $l$ plane $X$ . plane $X \|$ plane $Y$ and $l$ is not parallel to $Y$

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