Parallel Lines Parallel Lines and and

TransversalsTransversalsChapter 3-1Chapter 3-1

Lesson 3-1 Ideas/Vocabulary

• Identify the relationships between two lines or two planes.

• parallel lines

• Name angles formed by a pair of lines and a transversal.

• parallel planes

• skew lines

• transversal

• consecutive interior angles

• alternate exterior angles

• alternate interior angles

• corresponding angles

Preparation for Standard 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. (Key)

Parallel Lines //

• Two lines are // if they are coplanar and do not intersect.

Triangles are used to indicate

// lines

Skew Lines• Lines that do not intersect but are not

coplanar are called skew lines.

Parallel Planes

• Two planes that do not intersect.

Based on looks, find a line:1. // to AB and containing D2. to AB and containing D3. Skew to AB and containing D4. Name the plane(s) that contain D and appear to

be // to plane ABE

A D

E H

B C

GF

1. DC1. DC

2. AD2. AD

3. DH3. DH4. DCH or DGH or DCG4. DCH or DGH or DCG

Lesson 3-1 Example 1a

A. Name all planes that are parallel to plane AEF.

Identify Relationships

Answer: plane BHG

Lesson 3-1 Example 1b

__B. Name all segments that intersect AF.

Identify Relationships

Answer: EF, GF, DA, and BA__ __ __ __

Lesson 3-1 Example 1c

__C. Name all segments that are skew to AD.

Identify Relationships

Answer: FG, GB, EH, EC, and CH__ __ __ __ __

Lesson 3-1 CYP 1a

A B

C D

0% 0%0%0%

A. A

B. B

C. C

D. D

A.Name a plane that is parallel to plane RST.

plane WTZ

plane SYZ

plane WXY

plane QRX

Lesson 3-1 CYP 1b

A B

C D

0% 0%0%0%

B. Name a segment that intersects YZ.

XY

WX

QW

RS

A.

B.

C.

D.

0% 0%0%0%

Lesson 3-1 CYP 1c

C. Name a segment that is parallel to RX.

A.

B.

C.

D.

ZW

TZ

QR

ST

A. A

B. B

C. C

D. D

RX

ST

XW

QW

__

__

___

___

Lesson 3-1 CYP 1d

A B

C D

0% 0%0%0%

D. Name a segment that is skew to TZ.

__

Transversal• A line that intersects two or more coplanar

lines at different points.

t

1 2

3 4

5 6

7 8

t is a transversal

Lesson 3-1 Example 2a

Identify TransversalsA. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line v is a transversal.

Answer:

If the lines are extended, line v intersects lines u, w, x, and z.

Lesson 3-1 Example 2b

Identify TransversalsB. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line y is a transversal.

Answer:

lines u, w, x, z

Lesson 3-1 Example 2c

Identify TransversalsC. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line u is a transversal.

Answer:

lines v, x, y, z

Lesson 3-1 CYP 2a

A B

C D

0% 0%0%0%

A. A

B. B

C. C

D. D

A. HIKING A group of nature trails is shown. Identify the sets of lines to which line a is a transversal.

lines c, f

lines c, d, e

lines c, d, f

lines c, d, e, f

Lesson 3-1 CYP 2b

A B

C D

0% 0%0%0%

A. A

B. B

C. C

D. D

B. HIKING A group of nature trails is shown. Identify the sets of lines to which line b is a transversal.

no lines

lines c, f

lines c, d, e, f

lines a, c, d, e, f

Lesson 3-1 CYP 2c

A B

C D

0% 0%0%0%

A. A

B. B

C. C

D. D

C. HIKING A group of nature trails is shown. Identify the sets of lines to which line c is a transversal.

lines a, b

lines a, b, d, e, f

lines a, d, f

lines a, b, e

Lesson 3-1 CYP 2d

A B

C D

0% 0%0%0%

A. A

B. B

C. C

D. D

D. HIKING A group of nature trails is shown. Identify the sets of lines to which line d is a transversal.

lines e, f

lines a, b, f

lines a, b, c, e, f

lines a, b, c

Corresponding Angles• Two angles that occupy corresponding

positions.

t

1 2

3 4

5 6

7 8

1 and 5 are corresponding s

2 and 6 are corresponding s

3 and 7 are corresponding s

4 and 8 are corresponding s

Alternate Interior Angles• Two angles that lie between the two lines

on opposite sides of the transversal.

t

1 2

3 4

5 6

7 8

3 and 6 are Alt. Int. s

4 and 5 are Alt. Int. s

Alternate Exterior Angles• Two angles that lie outside the two lines on

opposite sides of the transversal.

t

1 2

3 4

5 6

7 8

1 and 8 are Alt. Ext. s

2 and 7 are Alt. Ext. s

Consecutive Interior Angles• Two angles that lie between the two lines

on the same side of the transversal.

t

1 2

3 4

5 6

7 8

3 and 5 are Consecutive Int. s

4 and 6 are Consecutive Int. s

Sometimes called Same Side Interior

Angles

Lesson 3-1 Example 3a

Identify Angle Relationships

Answer:

corresponding

A. Identify 7 and 3 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

Lesson 3-1 Example 3b

Identify Angle Relationships

B. Identify 8 and 2 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

Answer:

alternate exterior

Lesson 3-1 Example 3c

Identify Angle Relationships

C. Identify 4 and 11 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

Answer:

corresponding

Lesson 3-1 Example 3d

Identify Angle Relationships

D. Identify 7 and 1 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

Answer:

alternate exterior

Lesson 3-1 Example 3e

Identify Angle Relationships

E. Identify 3 and 9 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

Answer:

alternate interior

Lesson 3-1 Example 3f

Identify Angle Relationships

F. Identify 7 and 10 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

Answer:

consecutive interior

A. Identify 4 and 5.

Lesson 3-1 CYP 3a

A B

C D

0% 0%0%0%

A. A

B. B

C. C

D. D

alternate interior

alternate exterior

corresponding

consecutive interior

B. Identify 7 and 9.

Lesson 3-1 CYP 3b

A B

C D

0% 0%0%0%

A. A

B. B

C. C

D. D

alternate interior

alternate exterior

corresponding

consecutive interior

C. Identify 4 and 7.

Lesson 3-1 CYP 3c

A B

C D

0% 0%0%0%

A. A

B. B

C. C

D. D

alternate interior

alternate exterior

corresponding

consecutive interior

D. Identify 2 and 11.

Lesson 3-1 CYP 3d

A B

C D

0% 0%0%0%

A. A

B. B

C. C

D. D

alternate interior

alternate exterior

corresponding

consecutive interior

E. Identify 3 and 5.

Lesson 3-1 CYP 3e

A B

C D

0% 0%0%0%

A. A

B. B

C. C

D. D

alternate interior

alternate exterior

corresponding

consecutive interior

F. Identify 6 and 9.

Lesson 3-1 CYP 3e

A B

C D

0% 0%0%0%

A. A

B. B

C. C

D. D

alternate interior

alternate exterior

corresponding

consecutive interior

Practice

1 432

8 567

11

91012

Homework pg. 144

12-19,

24-35,

41-44