parallel lines and transversals
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Parallel Lines and Transversals. Geometry D – Section 3.1. 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. - PowerPoint PPT PresentationTRANSCRIPT
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Parallel Lines and Transversals
Geometry D – Section 3.1
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A
B
DC
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
AD
B
C
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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.
A
BC
D
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Parallel Lines and Transversals
For the rectangular box shown below, find
1. All planes parallel to plane CDE.
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Parallel Lines and Transversals
For the rectangular box shown below, find
1. All planes parallel to plane CDE.
Plane BAH (or any plane with BAHG).
A
H
E
G
F
B
CD
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Parallel Lines and Transversals
For the rectangular box shown below, find
2. The intersection of plane AHE and plane CFE.
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Parallel Lines and Transversals
For the rectangular box shown below, find
2. The intersection of plane AHE and plane CFE.
EDA
H
E
G
F
B
CD
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Parallel Lines and Transversals
For the rectangular box shown below, find
3. All segments parallel to CD.
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AB, GH, EF
Parallel Lines and Transversals
For the rectangular box shown below, find
3. All segments parallel to CD.
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Parallel Lines and Transversals
For the rectangular box shown below, find
4. All segments that intersect CF.
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Parallel Lines and Transversals
For the rectangular box shown below, find
4. All segments that intersect CF.
, ,
,
BC AC DC
GF EF
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Parallel Lines and Transversals
For the rectangular box shown below, find
5. All lines skew to GF.
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Parallel Lines and Transversals
For the rectangular box shown below, find
5. All lines skew to GF.
, ,
,
AB AC AB
AH DE
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.
t
mkjLines 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 -
t
kj
1
23
45
67
8
Exterior angles are on the exterior of the two lines cut by the transversal.
The exterior angles are:
1, 2, 7, 8
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Parallel Lines and Transversals
Identifying Angles -
t
kj
1
23
45
67
8
Interior angles are on the interior of the two lines cut by the transversal.
The interior angles are:
3, 4, 5, 6
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Parallel Lines and Transversals
Identifying Angles -
t
kj
1
23
45
67
8
Consecutive interior angles are on the interior of the two lines and on the same side of the transversal.
Consecutive interior angles are:
3 5,
4 6
and
or
and
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Parallel Lines and Transversals
Identifying Angles -
t
kj
1
23
45
67
8
Alternate interior angles are on the interior of the two lines and on opposite sides of the transversal.
Alternate interior angles are:
3 6,
4 5
and
or
and
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Parallel Lines and Transversals
Identifying Angles -
t
kj
1
23
45
67
8
Alternate exterior angles are on the exterior of the two lines and on opposite sides of the transversal.
Alternate exterior angles are:
1 8,
2 7
and
or
and
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Parallel Lines and Transversals
Identifying Angles -
t
kj
1
23
45
67
8
Consecutive interior angles are on the interior of the two lines and on the same side of the transversal.
Consecutive interior angles are:
3 5,
4 6
and
or
and
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Parallel Lines and Transversals
Identifying Angles -
t
kj
1
23
45
67
8
Corresponding angles are on the corresponding side of the two lines and on the same side of the transversal.
Corresponding angles are:1 5,
3 7,
2 6,
4 8
and
and
and or
and
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2. 2 and 10 are alternate interior angles.
Parallel Lines and Transversals
Identifying Angles – Check for Understanding
1 2 3 4
5678
9 10 11 12
13141516
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.
False - The angles are corresponding angles on transversal p.
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4. 1 and 15 are alternate exterior angles.
3. 3 and 5 are alternate interior angles.
Parallel Lines and Transversals
Identifying Angles – Check for Understanding
1 2 3 4
5678
9 10 11 12
13141516
Determine if the statement is true or false. If false, correct the statement.
False – The angles are vertical angles created by the intersection of q and r.
True - The angles are alternate exterior angles on transversal p.
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6. 10 and 11 are consecutive interior angles.
5. 6 and 12 are alternate interior angles.
Parallel Lines and Transversals
Identifying Angles – Check for Understanding
1 2 3 4
5678
9 10 11 12
13141516
Determine if the statement is true or false. If false, correct the statement.
True – The angles are alternate interior angles on transversal q.
True – The angles are consecutive interior angles on transversal s.
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Determine if the statement is true or false. If false, correct the statement. 7. 3 and 4 are
alternate exterior angles.
8. 16 and 14 are corresponding angles.
Parallel Lines and Transversals
Identifying Angles – Check for Understanding
1 2 3 4
5678
9 10 11 12
13141516
False – The angles are a linear pair with linear rays on line r.
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 odd2.2 / 22, 25, 28, 31, 34, 37, 40, 43, 46, 492.3 / 15-21 odd, 22-32 even2.4 / 13-29 odd2.5 / 15-33 odd2.6 / 16, 19, 22, 25, 28, 31, 34