3-1 Parallel Lines and Transversals

CCSS

Content StandardsG.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.Mathematical Practices1 Make sense of problems and persevere in solving them.3 Construct viable arguments and critique the reasoning of others.

Then/Now

You used angle and line segment relationships to prove theorems.

• Identify relationships between two lines or two planes.

• Name angle pairs formed by parallel lines and transversals.

Vocabulary

• parallel lines• skew lines• parallel planes• transversal• interior angles• exterior angles

• consecutive interior angles

• alternate interior angles

• alternate exterior angles

• corresponding angles

Concept

Vocabulary

• transversal:

a line that intersects two or more coplanar lines at two different points

Example 1

Answer: AD, EH, FG

A. Name all segments parallel to BC.

Example 1B. Name a segment skew to EH.

Answer: AB, CD, BG, or CF

C. Name a plane parallel to plane ABG.

Example 1

Answer: plane CDE

Example 1a

A. plane WTZ

B. plane SYZ

C. plane WXY

D. plane QRX

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

Example 1bB. Name a segment that

intersects YZ.

A. XY

B. WX

C. QW

D. RS

Example 1cC. Name a segment that is

parallel to RX.

A. ZW

B. TZ

C. QR

D. ST

Concept

Vocabulary

• Interior angles

Example:

Vocabulary

• Exterior angles

Example:

Vocabulary

• Consecutive interior angles

Example:

Vocabulary

• Alternate interior angles

Example:

Vocabulary

• Alternate exterior angles

Example:

Vocabulary

• Corresponding angles

Example:

Example 2A. Classify the relationship between 2 and 6 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

Answer: corresponding

Example 2B. Classify the relationship between 1 and 7 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

Answer: alternate exterior

Example 2C. Classify the relationship between 3 and 8 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

Answer: consecutive interior

Example 2D. Classify the relationship between 3 and 5 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

Answer: alternate interior

Example 2a

A. alternate interior

B. alternate exterior

C. corresponding

D. consecutive interior

A. Classify the relationship between 4 and 5.

Example 2b

A. alternate interior

B. alternate exterior

C. corresponding

D. consecutive interior

B. Classify the relationship between 7 and 9.

Example 2c

A. alternate interior

B. alternate exterior

C. corresponding

D. consecutive interior

C. Classify the relationship between 4 and 7.

Example 2d

A. alternate interior

B. alternate exterior

C. corresponding

D. consecutive interior

D. Classify the relationship between 2 and 11.

Example 3A. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 1 and 2. Then classify the relationship between the pair of angles.

Answer: The transversal connecting 1 and 2 is line v. These are corresponding angles.

Example 3B. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 2 and 3. Then classify the relationship between the pair of angles.

Answer: The transversal connecting 2 and 3 is line v. These are alternate interior angles.

Example 3C. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 4 and 5. Then classify the relationship between the pair of angles.

Answer: The transversal connecting 4 and 5 is line y. These are consecutive interior angles.