Parallel Lines and Transversals

Geometry D – Section 3.1

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

Parallel Lines and Transversals

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

AB || CD

AD

B

C

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

Parallel Lines and Transversals

For the rectangular box shown below, find

1. All planes parallel to plane CDE.

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

Parallel Lines and Transversals

For the rectangular box shown below, find

2. The intersection of plane AHE and plane CFE.

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

Parallel Lines and Transversals

For the rectangular box shown below, find

3. All segments parallel to CD.

AB, GH, EF

Parallel Lines and Transversals

For the rectangular box shown below, find

3. All segments parallel to CD.

Parallel Lines and Transversals

For the rectangular box shown below, find

4. All segments that intersect CF.

Parallel Lines and Transversals

For the rectangular box shown below, find

4. All segments that intersect CF.

, ,

,

BC AC DC

GF EF

Parallel Lines and Transversals

For the rectangular box shown below, find

5. All lines skew to GF.

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.

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.

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

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

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

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

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

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

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

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.

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.

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.

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.

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