This document provides definitions and examples related to parallel and perpendicular lines. It defines parallel lines as lines in the same plane that do not intersect, and skew lines as lines in different planes that do not intersect. It also defines angles formed by parallel lines cut by a transversal, such as corresponding angles and alternate interior angles. Examples classify line segments and planes as parallel or skew, and identify angle relationships.

1. CHAPTER
3
Parallel and
Perpendicular Lines
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2. SECTION 3-1
Parallel Lines and Transversals
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3. ESSENTIAL
QUESTIONS
How do you identify the relationships between two lines or
two planes?
How do you name angle pairs formed by parallel lines and
transversals?
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4. VOCABULARY
1. Parallel Lines:
2. Skew Lines:
3. Parallel Planes:
4. Transversal:
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5. VOCABULARY
1. Parallel Lines: Two or more lines in the same plane that do not
intersect
2. Skew Lines:
3. Parallel Planes:
4. Transversal:
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6. VOCABULARY
1. Parallel Lines: Two or more lines in the same plane that do not
intersect
2. Skew Lines: Two or more lines that are in different planes and
do not intersect
3. Parallel Planes:
4. Transversal:
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7. VOCABULARY
1. Parallel Lines: Two or more lines in the same plane that do not
intersect
2. Skew Lines: Two or more lines that are in different planes and
do not intersect
3. Parallel Planes: Two or more planes that do not intersect
4. Transversal:
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8. VOCABULARY
1. Parallel Lines: Two or more lines in the same plane that do not
intersect
2. Skew Lines: Two or more lines that are in different planes and
do not intersect
3. Parallel Planes: Two or more planes that do not intersect
4. Transversal: A line that intersects two other coplanar lines at
two different points
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9. VOCABULARY
5. Interior Angles:
6. Exterior Angles:
7. Consecutive Interior Angles:
8. Alternate Interior Angles:
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10. VOCABULARY
5. Interior Angles: Angles that are formed in the region between
two lines being intersected by a transversal
6. Exterior Angles:
7. Consecutive Interior Angles:
8. Alternate Interior Angles:
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11. VOCABULARY
5. Interior Angles: Angles that are formed in the region between
two lines being intersected by a transversal
6. Exterior Angles: Angles that are formed in the region outside of
the two lines being intersected by a transversal
7. Consecutive Interior Angles:
8. Alternate Interior Angles:
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12. VOCABULARY
5. Interior Angles: Angles that are formed in the region between
two lines being intersected by a transversal
6. Exterior Angles: Angles that are formed in the region outside of
the two lines being intersected by a transversal
7. Consecutive Interior Angles: Interior angles that are on the
same side of the transversal, thus being “next” to each other
8. Alternate Interior Angles:
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13. VOCABULARY
5. Interior Angles: Angles that are formed in the region between
two lines being intersected by a transversal
6. Exterior Angles: Angles that are formed in the region outside of
the two lines being intersected by a transversal
7. Consecutive Interior Angles: Interior angles that are on the
same side of the transversal, thus being “next” to each other
8. Alternate Interior Angles: Nonadjacent interior angles that are
on opposite sides of the transversal
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14. VOCABULARY
9. Alternate Exterior Angles:
10. Corresponding Angles:
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15. VOCABULARY
9. Alternate Exterior Angles: Nonadjacent exterior angles that are
on opposite sides of the transversal
10. Corresponding Angles:
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16. VOCABULARY
9. Alternate Exterior Angles: Nonadjacent exterior angles that are
on opposite sides of the transversal
10. Corresponding Angles: Angles that are on the same side of the
transversal and on the same side of the lines being intersected
by the transversal; these angles have the same position
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17. EXAMPLE 1
Identify each of the following using the box.
a. All segments parallel to BC
b. A segment that is skew to EH
c. A plane that is parallel to plane ABG
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18. EXAMPLE 1
Identify each of the following using the box.
a. All segments parallel to BC
FG, AD, EH
b. A segment that is skew to EH
c. A plane that is parallel to plane ABG
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19. EXAMPLE 1
Identify each of the following using the box.
a. All segments parallel to BC
FG, AD, EH
b. A segment that is skew to EH
DC, CF, AB, or BG
c. A plane that is parallel to plane ABG
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20. EXAMPLE 1
Identify each of the following using the box.
a. All segments parallel to BC
FG, AD, EH
b. A segment that is skew to EH
DC, CF, AB, or BG
c. A plane that is parallel to plane ABG
Plane DEC
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21. EXAMPLE 2
Refer to the figure below. Classify the relationship between
each pair of angles as alternate interior, alternate exterior,
corresponding, or consecutive interior angles.
a. ∠2 and ∠6 b. ∠1 and ∠7
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22. EXAMPLE 2
Refer to the figure below. Classify the relationship between
each pair of angles as alternate interior, alternate exterior,
corresponding, or consecutive interior angles.
a. ∠2 and ∠6 b. ∠1 and ∠7
Corresponding Angles
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23. EXAMPLE 2
Refer to the figure below. Classify the relationship between
each pair of angles as alternate interior, alternate exterior,
corresponding, or consecutive interior angles.
a. ∠2 and ∠6 b. ∠1 and ∠7
Corresponding Angles Alternate Exterior Angles
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24. EXAMPLE 2
Refer to the figure below. Classify the relationship between
each pair of angles as alternate interior, alternate exterior,
corresponding, or consecutive interior angles.
c. ∠3 and ∠8 d. ∠3 and ∠5
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25. EXAMPLE 2
Refer to the figure below. Classify the relationship between
each pair of angles as alternate interior, alternate exterior,
corresponding, or consecutive interior angles.
c. ∠3 and ∠8 d. ∠3 and ∠5
Consecutive Interior Angles
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26. EXAMPLE 2
Refer to the figure below. Classify the relationship between
each pair of angles as alternate interior, alternate exterior,
corresponding, or consecutive interior angles.
c. ∠3 and ∠8 d. ∠3 and ∠5
Consecutive Interior Angles Alternate Interior Angles
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27. EXAMPLE 3
The driveways at a bus station are shown. Identify the
transversal connecting each pair of angles in the figure. Then
classify the relationship between each pair of angles.
a. ∠1 and ∠2 b. ∠2 and ∠3
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28. EXAMPLE 3
The driveways at a bus station are shown. Identify the
transversal connecting each pair of angles in the figure. Then
classify the relationship between each pair of angles.
a. ∠1 and ∠2 b. ∠2 and ∠3
v; Corresponding
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29. EXAMPLE 3
The driveways at a bus station are shown. Identify the
transversal connecting each pair of angles in the figure. Then
classify the relationship between each pair of angles.
a. ∠1 and ∠2 b. ∠2 and ∠3
v; Corresponding v; Alternate Interior
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30. EXAMPLE 3
The driveways at a bus station are shown. Identify the
transversal connecting each pair of angles in the figure. Then
classify the relationship between each pair of angles.
c. ∠4 and ∠5
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31. EXAMPLE 3
The driveways at a bus station are shown. Identify the
transversal connecting each pair of angles in the figure. Then
classify the relationship between each pair of angles.
c. ∠4 and ∠5
y; Consecutive Interior
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32. CHECK YOUR
UNDERSTANDING
Check out the problems on p. 173 #1-12.
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33. PROBLEM SET
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34. PROBLEM SET
p. 174 #13-45 odd
“It has long been an axiom of mine that the little things are
infinitely the most important.” - Sir Arthur Conan Doyle
Tuesday, December 13, 2011