Parallel Lines and Transversals

Parallel Lines and Transversals

Geometry D – Section 3.1

A

B

DC


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

AD

B

C


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


For the rectangular box shown below, find

1. All planes parallel to plane CDE.



1. All planes parallel to plane CDE.

Plane BAH (or any plane with BAHG).

A

H

E

G

F

B

CD



2. The intersection of plane AHE and plane CFE.



2. The intersection of plane AHE and plane CFE.

EDA

H

E

G

F

B

CD



3. All segments parallel to CD.

AB, GH, EF



3. All segments parallel to CD.



4. All segments that intersect CF.



4. All segments that intersect CF.

, ,

,

BC AC DC

GF EF



5. All lines skew to GF.



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.


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.


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



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



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



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



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



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



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.


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.




1 2 3 4

5678

9 10 11 12

13141516


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.




1 2 3 4

5678

9 10 11 12

13141516


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.



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.


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

Parallel Lines and Transversals

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