Parallel Lines and Transversals

1
Parallel Lines and Transversals

• Geometry D Section 3.1

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Parallel Lines and Transversals
What would you call two lines which do not
intersect?
Parallel
A solid arrow placed on two lines of a diagram
indicate the lines are parallel.
The symbol is used to indicate parallel
lines.
AB CD
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Parallel Lines and Transversals
A slash through the parallel symbol
indicates the lines are not parallel.
AB CD
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Parallel Lines and Transversals
Skew Lines
Two lines are skew if they are not in the same
plane and do not intersect.
AB does not intersect CD . Since the lines are
not in the same plane, they are skew lines.
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Parallel Lines and Transversals
For the rectangular box shown below, find

• All planes parallel to plane CDE.

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Parallel Lines and Transversals
For the rectangular box shown below, find

• All planes parallel to plane CDE.

Plane BAH (or any plane with BAHG).
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Parallel Lines and Transversals
For the rectangular box shown below, find

• The intersection of plane AHE and plane CFE.

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Parallel Lines and Transversals
For the rectangular box shown below, find

• The intersection of plane AHE and plane CFE.

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Parallel Lines and Transversals
For the rectangular box shown below, find

• All segments parallel to CD.

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Parallel Lines and Transversals
For the rectangular box shown below, find

• All segments parallel to CD.

AB, GH, EF
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Parallel Lines and Transversals
For the rectangular box shown below, find

• All segments that intersect CF.

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Parallel Lines and Transversals
For the rectangular box shown below, find

• All segments that intersect CF.

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Parallel Lines and Transversals
For the rectangular box shown below, find

• All lines skew to GF.

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Parallel Lines and Transversals
For the rectangular box shown below, find

• All lines skew to GF.

Segments HE, AD, and BC are or in the same
plane. Segments GH, EF, BG and CF intersect and
are in the same plane. These segments are not
skew to GF.
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Parallel Lines and Transversals
Transversal -
A transversal is a line which intersects two or
more lines in a plane. The intersected lines do
not have to be parallel.
Lines j, k, and m are intersected by line t.
Therefore, line t is a transversal of lines j, k,
and m.
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Parallel Lines and Transversals
Identifying Angles -
Exterior angles are on the exterior of the two
lines cut by the transversal.
1
3
5
7
2
4
6
8
The exterior angles are
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Parallel Lines and Transversals
Identifying Angles -
Interior angles are on the interior of the two
lines cut by the transversal.
1
3
5
7
2
4
6
8
The interior angles are
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Parallel Lines and Transversals
Identifying Angles -
Consecutive interior angles are on the interior
of the two lines and on the same side of the
transversal.
1
3
5
7
2
4
6
8
Consecutive interior angles are
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Parallel Lines and Transversals
Identifying Angles -
Alternate interior angles are on the interior of
the two lines and on opposite sides of the
transversal.
1
3
5
7
2
4
6
8
Alternate interior angles are
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Parallel Lines and Transversals
Identifying Angles -
Alternate exterior angles are on the exterior of
the two lines and on opposite sides of the
transversal.
1
3
5
7
2
4
6
8
Alternate exterior angles are
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Parallel Lines and Transversals
Identifying Angles -
Consecutive interior angles are on the interior
of the two lines and on the same side of the
transversal.
1
3
5
7
2
4
6
8
Consecutive interior angles are
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Parallel Lines and Transversals
Identifying Angles -
Corresponding angles are on the corresponding
side of the two lines and on the same side of the
transversal.
1
3
5
7
2
4
6
8
Corresponding angles are
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Parallel Lines and Transversals
Identifying Angles Check for Understanding
Determine if the statement is true or false. If
false, correct the statement.
1. Line r is a transversal of lines p and q.
True Line r intersects both lines in a plane.
4
3
2
1
5
6
7
8
2. 2 and 10 are alternate interior
angles.
9
10
False - The angles are corresponding angles on
transversal p.
11
12
15
13
14
16
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Parallel Lines and Transversals
Identifying Angles Check for Understanding
Determine if the statement is true or false. If
false, correct the statement.
3. 3 and 5 are alternate interior angles.
False The angles are vertical angles created by
the intersection of q and r.
4
3
2
1
5
6
7
8
4. 1 and 15 are alternate exterior
angles.
9
10
11
12
15
13
14
16
True - The angles are alternate exterior angles
on transversal p.
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Parallel Lines and Transversals
Identifying Angles Check for Understanding
Determine if the statement is true or false. If
false, correct the statement.
5. 6 and 12 are alternate interior
angles.
True The angles are alternate interior angles
on transversal q.
4
3
2
1
5
6
7
8
6. 10 and 11 are consecutive interior
angles.
9
10
11
12
15
13
14
16
True The angles are consecutive interior angles
on transversal s.
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Parallel Lines and Transversals
Identifying Angles Check for Understanding
Determine if the statement is true or false. If
false, correct the statement.
7. 3 and 4 are alternate exterior angles.
False The angles are a linear pair with linear
rays on line r.
4
3
2
1
5
6
7
8
8. 16 and 14 are corresponding angles.
9
10
11
12
15
13
14
16
True The angles are corresponding on
transversal s.
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Parallel Lines and Transversals
Assignment 3.1 - 16, 20, 24, 26, 28-33, 34-44
even, 47, 51, 54, 59, 60
Reassessment Problems 2.1 / 15 - 27 odd 2.2 /
22, 25, 28, 31, 34, 37, 40, 43, 46, 49 2.3 /
15-21 odd, 22-32 even 2.4 / 13-29 odd 2.5 /
15-33 odd 2.6 / 16, 19, 22, 25, 28, 31, 34