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Parallel Lines and Transversals. 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 transversals2
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

parallel lines and transversals3
Parallel Lines and Transversals

A slash through the parallel symbol || indicates the lines are not parallel.

AB || CD

parallel lines and transversals4
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.

parallel lines and transversals5
Parallel Lines and Transversals

For the rectangular box shown below, find

  • All planes parallel to plane CDE.
parallel lines and transversals6
Parallel Lines and Transversals

For the rectangular box shown below, find

  • All planes parallel to plane CDE.

Plane BAH (or any plane with BAHG).

parallel lines and transversals7
Parallel Lines and Transversals

For the rectangular box shown below, find

  • The intersection of plane AHE and plane CFE.
parallel lines and transversals8
Parallel Lines and Transversals

For the rectangular box shown below, find

  • The intersection of plane AHE and plane CFE.
parallel lines and transversals9
Parallel Lines and Transversals

For the rectangular box shown below, find

  • All segments parallel to CD.
parallel lines and transversals10
Parallel Lines and Transversals

For the rectangular box shown below, find

  • All segments parallel to CD.

AB, GH, EF

parallel lines and transversals11
Parallel Lines and Transversals

For the rectangular box shown below, find

  • All segments that intersect CF.
parallel lines and transversals12
Parallel Lines and Transversals

For the rectangular box shown below, find

  • All segments that intersect CF.
parallel lines and transversals13
Parallel Lines and Transversals

For the rectangular box shown below, find

  • All lines skew to GF.
parallel lines and transversals14
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.

parallel lines and transversals15
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.

parallel lines and transversals16
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:

parallel lines and transversals17
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:

parallel lines and transversals18
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:

parallel lines and transversals19
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:

parallel lines and transversals20
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:

parallel lines and transversals21
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:

parallel lines and transversals22
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:

parallel lines and transversals23
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

8

7

2. 2 and 10 are alternate interior angles.

9

10

False - The angles are corresponding angles on transversal p.

11

12

15

16

14

13

parallel lines and transversals24
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

8

7

4. 1 and 15 are alternate exterior angles.

9

10

11

12

15

16

14

13

True - The angles are alternate exterior angles on transversal p.

parallel lines and transversals25
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

8

7

6. 10 and 11 are consecutive interior angles.

9

10

11

12

15

16

14

13

True – The angles are consecutive interior angles on transversal s.

parallel lines and transversals26
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

8

7

8. 16 and 14 are corresponding angles.

9

10

11

12

15

16

14

13

True – The angles are corresponding on transversal s.

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