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GEOMETRYChapter 3: 3-1: Parallel Lines and Transversals
Do Now: • Quick Ponder:
• What are parallel lines? How can we tell if two lines are parallel?
• Review: • If you are tired in class, then you may fall asleep
• What is the inverse of this statement?
• What is the converse of this statement?
Definitions: • Parallel Lines: are coplanar lines that do not intersect.
• Notation:
• Picture: Arrows are used to indicate that lines are parallel.
Definitions (continued) • Skew Lines: Are lines that do not intersect and are not
coplanar.
• No Notation
• Picture:
Definitions (Continued) • Parallel Planes: are planes that do not intersect.
• Notation: None
• Picture:
Example 1: • Identify each of the following using the wedge of cheese
below.
• a) All segments parallel to JP
• b) A segment skew to KL
• c) A plane parallel to plane PQR
Example 1: Answers • Identify each of the following using the wedge of cheese
below.
• a) All segments parallel to JP
- KQ and LR• b) A segment skew to KL
- JP, PQ, PR • c) A plane parallel to plane PQR
- Plane JKL
Example 2: • In the figure, assume that the lines and planes that
appear to be parallel are parallel.
• Which segments are parallel to AB?
• Which segments are skew to CD?
• What are two pairs of parallel planes?
• What are two segments parallel to plane BCGF?
Example 2: Answers • In the figure, assume that the lines and planes that
appear to be parallel are parallel.
• Which segments are parallel to AB?
- CD, EF • Which segments are skew to CD?
- BF, AE, EF, EH, FG
What are two pairs of parallel planes?
- Plane ABCD is parallel to Plane EFGH
- Plane ADHE is parallel to EFGC• What are two segments parallel to plane BCGF?
• AE and HD
Definition: • Transversal: A line that intersects two or more coplanar
lines at two different points.
• Notation: None
• Picture: t is a transversal
of lines l and m
Definitions: • Interior Angles: Angles that lie in the region between two
lines.
Here interior angles are:
Definitions: • Interior Angles: Angles that lie in the region between two
lines.
Here interior angles are:
<3, <4, <5, <6
Definitions: • Exterior Angles: Angles that lie in the region outside of two
lines.
Here exterior angles are:
Definitions: • Exterior Angles: Angles that lie in the region outside of two
lines.
Here exterior angles are:
<1, <2, <7, <8
Definitions: • Consecutive Interior Angles: Interior Angles that lie on the
same side of a transversal.
Here consecutive interior
angles are:
Definitions: • Consecutive Interior Angles: Interior Angles that lie on the
same side of a transversal.
Here consecutive interior
angles are:
<3 and <6
<4 and <5
Definitions: • Alternate Interior Angles: are nonadjacent interior angles
that lie on opposite sides of a transversal.
Alternate Interior Angles:
Definitions: • Alternate Interior Angles: are nonadjacent interior angles
that lie on opposite sides of a transversal.
Alternate Interior Angles:
<4 and <6
<5 and <3
Definitions: • Alternate Exterior Angles: are nonadjacent exterior angles
that lie on opposite sides of a transversal.
Alternate Exterior Angles:
Definitions: • Alternate Exterior Angles: are nonadjacent exterior angles
that lie on opposite sides of a transversal.
Alternate Exterior Angles:
<1 and <7
<2 and <8
Definitions: • Corresponding Angles: lie on the same side of a
transversal and on the same side of the two lines the transversal intersects.
Corresponding angles:
Definitions: • Corresponding Angles: lie on the same side of a
transversal and on the same side of the two lines the transversal intersects.
Corresponding angles:
<1 and <5
<4 and <8
<2 and <6
<3 and <7
Example 3:
Example 4:
Practice Problems• Try some on your own/in table groups. • As always if you are confused please don’t hesitate to ask
me questions.
Exit Ticket
Name an example of each:
1.Corresponding Angles2.Alternate Exterior Angles3.Consecutive Interior Angles4.Alternate Interior Angles