# Geometry

## Educators DP

### Problem 1

Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles.
$$\angle 2 \text { and } \angle 6$$ Salamat A.

### Problem 2

Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles.
$$\angle 8 \text { and } \angle 6$$

DP
Daniel P.

### Problem 3

Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles.
$$\angle 2 \text { and } \angle 3$$ Salamat A.

### Problem 4

Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles.
$$\angle 3 \text { and } \angle 7$$

DP
Daniel P.

### Problem 5

Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles.
$$\angle 5 \text { and } \angle 7$$ Salamat A.

### Problem 6

Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles.
$$\angle 3 \text { and } \angle 1$$

DP
Daniel P.

### Problem 7

Name the two lines and the transversal that form each pair of angles.
$$\angle 2 \text { and } \angle 3$$ Salamat A.

### Problem 8

Name the two lines and the transversal that form each pair of angles.
$$\angle 1 \text { and } \angle 4$$

DP
Daniel P.

### Problem 9

Name the two lines and the transversal that form each pair of angles.
$$\angle P \text { and } \angle P S R$$ Salamat A.

### Problem 10

Name the two lines and the transversal that form each pair of angles.
$$\angle 5 \text { and } \angle P S R$$

DP
Daniel P.

### Problem 11

Name the two lines and the transversal that form each pair of angles.
$$\angle 5 \text { and } \angle P Q R$$ Salamat A.

### Problem 12

Classify each pair of angles as alternate interior, same-side interior, or corresponding angles.
$$\angle E B A \text { and } \angle F C B$$

DP
Daniel P.

### Problem 13

Classify each pair of angles as alternate interior, same-side interior, or corresponding angles.
$$\angle D C H \text { and } \angle C B J$$ Salamat A.

### Problem 14

Classify each pair of angles as alternate interior, same-side interior, or corresponding angles.
$$\angle F C B \text { and } \angle C B L$$

DP
Daniel P.

### Problem 15

Classify each pair of angles as alternate interior, same-side interior, or corresponding angles.
$$\angle F C L \text { and } \angle B L C$$ Salamat A.

### Problem 16

Classify each pair of angles as alternate interior, same-side interior, or corresponding angles.
$$\angle H C B \text { and } \angle C B J$$

DP
Daniel P.

### Problem 17

Classify each pair of angles as alternate interior, same-side interior, or corresponding angles.
$$\angle G C H \text { and } \angle G L J$$ Salamat A.

### 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?

DP
Daniel P.

### 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? Salamat A.

### 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?

DP
Daniel P.

### 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.

DP
Daniel P.

### Problem 23

Exercises $23-29$ refer to the diagram in Step 2 of Exercise $22 .$
Name five lines that appear to be parallel to $\overline{A G}$ . Salamat A.

### Problem 24

Exercises $23-29$ refer to the diagram in Step 2 of Exercise $22 .$
Name three lines that appear to be parallel to $\overline{A B}$ .

DP
Daniel P.

### 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 $\overrightarrow{A F}$ .

DP
Daniel P.

### 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?

DP
Daniel P.

### 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.

DP
Daniel P.

### 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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