**Unit 2 Lesson 4**

Parallel Lines & Transversals

Parallel Lines & Transversals

Consecutive Interior Angles Theorem

Guided Practice

Use the diagram below for each of the two questions:

Corresponding Angles

Postulate

If then,

Alternate Interior Angles Theorem

Example 1:

Identify Congruent Angles

Example 2:

Use Properties of

Parallel Lines

Find the value of x.

Alternate Exterior Angles Theorem

If then,

If then,

If Angle 1 = 110, find the value of the remaining numbered angles. Be prepared to explain how your answer is related to Angle 1 or a previously answered numbered angle.

**Jennifer Priebe and Wilson Cisneros**

Investigations for Lesson 2.6

Exterior

Interior

Exterior

The two regions not between the lines is referred to as the exterior.

The region between the lines is referred to as the interior.

Two lines divide the plane into three regions.

Parallel Lines and Transversals

congruent

6

7

5

4

3

1

8

2

Parallel Lines and Transversals

supplementary

8

6

7

5

4

3

2

1

Parallel Lines and Transversals

supplementary

4

3

2

1

Parallel Lines and Transversals

7

8

5

6

congruent

Objective: Discover relationships between special pairs of angles created by a pair of parallel lines cut by a transversal.

Lesson 4 Special Angles on Parallel Lines

Complete Investigations 1 & 2 WS

Complete conjectures

8

6

7

5

4

3

2

1

Parallel Lines and Transversals

Parallel Lines and Transversals

congruent

same side exterior angles- SSE

linear pair of angles- LP

vertical angles- VA

Types of angle pairs formed when

a transversal cuts two parallel lines.

same side interior angles- SSI

corresponding angles - CA

alternate exterior angles- AEA

alternate interior angles- AIA

Parallel Lines w/a transversal AND

Angle Pair Relationships

Parallel Lines and Transversals

alternate interior angles

5 and 10

alternate exterior angles

14 and 1

same side exterior angles

1 and 4

corresponding angles

9 and 1

alternate exterior angles

8 and 1

vertical angles

6 and 1

corresponding angles

3 and 1

s || t and c || d.

Name all the angles that are congruent to 1.

Give a reason for each answer.

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

d

c

t

s

Parallel Lines and Transversals

40°

120°

Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements.

Another practice problem

Exterior

Exterior

Interior

If the lines are not parallel, these angle relationships

DO NOT EXIST.

3

8

7

5

6

2

4

1

♥Alternate Interior Angles

are CONGRUENT

♥Alternate Exterior Angles are CONGRUENT

♥Same Side Interior Angles are SUPPLEMENTARY

♥Same Side Exterior Angles are SUPPLEMENTARY

♥Corresponding Angles are

CONGRUENT

SUMMARY: WHEN THE LINES ARE PARALLEL

Alternate Interior Angles are congruent

STANDARDS

Content: G.CO.C.9

Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent.

Anchor Standard

CCSS.ELA-Literacy.CCRA.SL.4

Present information, findings, and supporting evidence such that listeners can follow the line of reasoning and the organization, development, and style are appropriate to task, purpose, and audience.

LEARNING OUTCOME (Objective):

• Students will be able to prove theorems about lines and angles by using the relationship between special pairs of angles created by a pair of parallel lines cut by a transversal including Vertical, corresponding, same side exterior, same side interior, alternate interior, and alternate exterior angles.

Do Now (25 min)

Students will use their IPad to research how engineers and architects

use the Vertical Angles Theorem and Supplementary Angles and their importance.

1. In your IPad:

a.

From last class, you learned about the Vertical Angles Theorem and Supplementary Angles. Conduct a research on how engineers and architects use vertical angles and supplementary angles.

b.

Write a description of how engineers and architects use both types of angles. (complete sentences)

c.

Explain the importance of using supplementary angles and vertical angles.

d.

When instructed by Mr. Cisneros, Think-Pair-Share with your group.

Elements of the 21st Century Classroom

1. Students take responsibility of their learning

Group work: ( 35 min)

a. The teacher partners students for the following activity.

• You are given the “Little Man’s Journey to the Door” map.

• Using the following:

Alternate Interior Angles Vertical Angles

Alternate Exterior Angles

Same Side Interior Angles Corresponding Angles____

Same Side Exterior Angles

• Take the Little Man to the door.

• Highlight or color each angle the Little Man lands on as you go on.

• Create a list of what kind of move you did i.e. 1) Vertical Angles 2) Alt. Ext. Angles

• You cannot use the same movement twice back to back.

• You cannot move Little Man to an angle that is more than 1 parallel line away.

Elements of the 21st Century Classroom

2. Student-centric

3. Active Learning

4. Students understand and follow the rules and procedures

Group

Activity

THINK-PAIR-SHARE

WITH YOUR GROUP

1. Students explain which angles they used most

2. Students ask different questions to other group members i.e. which angle was most difficult to use?

Elements of the 21st Century Classroom

5. Collaborative learning

Write a Reflection on what you learned today.

Explain what you learned in detail.

provide an example. (Types of angles)

was there any difficult part of the lesson?

INDEPENDENT PRACTICE

Complete the worksheet provided