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Parallel Lines and Transversals

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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

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

AB || CD

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.

For the rectangular box shown below, find

- All planes parallel to plane CDE.

For the rectangular box shown below, find

- All planes parallel to plane CDE.

Plane BAH (or any plane with BAHG).

For the rectangular box shown below, find

- The intersection of plane AHE and plane CFE.

For the rectangular box shown below, find

- The intersection of plane AHE and plane CFE.

For the rectangular box shown below, find

- All segments parallel to CD.

For the rectangular box shown below, find

- All segments parallel to CD.

AB, GH, EF

For the rectangular box shown below, find

- All segments that intersect CF.

For the rectangular box shown below, find

- All segments that intersect CF.

For the rectangular box shown below, find

- All lines skew to GF.

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.

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.

Identifying Angles -

Exterior angles are on the exterior of the two lines cut by the transversal.

1

3

5

7

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4

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8

The exterior angles are:

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:

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:

Identifying Angles -

Alternate interior angles are on the interior of the two lines and on opposite sides of the transversal.

1

3

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7

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Alternate interior angles are:

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

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8

Alternate exterior angles are:

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:

Identifying Angles -

Corresponding angles are on the corresponding side of the two lines and on the same side of the transversal.

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Corresponding angles are:

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.

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3

2

1

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2. 2 and 10 are alternate interior angles.

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10

False - The angles are corresponding angles on transversal p.

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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.

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3

2

1

5

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7

4. 1 and 15 are alternate exterior angles.

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

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.

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3

2

1

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6. 10 and 11 are consecutive interior angles.

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10

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

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.

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3

2

1

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8. 16 and 14 are corresponding angles.

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True – The angles are corresponding on transversal s.