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# Angle Relationships Along Parallel Lines Continued

Lesson 18 of 23

## Objective: Students will be able to understand and prove angle relationships along parallel lines cut by a transversal through the application of transformations

*55 minutes*

#### Continuing the Activity

*40 min*

Watch a short video explaining the rational for this lesson and why I have chosen to apply transformations to parallel lines cut by a transversal.

Clarifying and Sharing Learning Goals

Always begin by clarifying for the students what it is they will be learning from the activity today.

The learning goals for today are to continue the activity and begin to really focus on learning about angle pair relationships. The graphs should be complete on each student’s paper and they should be ready to at least begin at question 5 with exploring corresponding angle pairs. The goal is that students will use tracing paper to copy one angle and then as the definition of congruent suggests, move the tracing paper over the second angle and check for congruence. Once congruence has been determined for most of the angle pairs, it is then the student’s job to write a transformation rule that would move the tracing paper to sit over the second angle. You want students to use the definition of congruence to find relationships and then use detailed transformations to prove these angles are connected. These goals clearly address the following math standards:

** **

**8.G.A.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.**

** **

**8.G.A.5 Use informal arguments to establish facts about the **angle sum and exterior angle of triangles,** about the angles created when parallel lines are cut by a transversal, **and the angle-angle criterion for similarity of triangles.

Working in Cooperative Groups to Make Connections

Allow students time to work through questions five, six, and seven. Students should work within their partnership or small group to correctly answer these questions. While students are graphing, move about the room formatively assessing progress and providing feedback that will move your students’ learning forward. To better understand how I group students into cooperative teams and how I provide feedback to students, click on the links below to watch a short video on each strategy.

**Cooperative Grouping Explained**

**Providing feedback that moves learning forward **

After allowing time for groups to working through questions five, six, and seven bring the whole class back together and hold a mini wrap up for students to share what they have learned. This mini wrap up should be student lead and student focused so student feel that they own their own learning and can discuss and defend it to others. Click below to watch a short video about how I incorporate student ownership of learning in my classroom.

**Activating students as owners of their own learning**

I call this time of students presenting their work a “mini wrap-up” because I do not spend long periods of time closing a lesson at the end of the class period. We use small lesson closers after a small chunk of material has been completed.

Math Practice Standards

Applying the strategy of mini-wrap ups that are student centered will directly bring math practice standard 3 into the lesson.

**MP3 Construct viable arguments and critique the reasoning of others**

Allowing students to work in groups, with hands-on materials if they want to use the materials, to explore angle relationships and prove they exist with detailed transformation directions really addresses several math practice standards:

**MP5 Use appropriate tools strategically. **

**MP6 Attend to precision. **

Working in Cooperative Groups to Make Connections Continued

Once you conclude a mini wrap up of corresponding angles, allow students to work within their cooperative groups to finish questions eight, nine, and ten which ask them to explore alternate interior angles. Again as students work together to share ideas and become resources for each other, make sure you are circulating about the room providing feedback that moves their learning forward as well. Click below to watch a short video on how students provide feedback to one another within small groups.

**Activating students as resources for one another**

**Where to End the Lesson**

The goal for the second day is to reach at least question 10 and discuss the answers to these questions in a mini wrap-up before the end of class. Of course students will work at their own pace and that is encouraged. You just want to at least get everyone through question 10 by the end of the second class period.

##### Resources (10)

#### Resources

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- LESSON 1: Introduction to Transformations using Play-dough
- LESSON 2: Hands-on Exploring Translations in the Plane
- LESSON 3: Hands-on Exploring Translations in the Plane Continued
- LESSON 4: Hands-on Exploring the Movement of Reflections in the Plane
- LESSON 5: Hands on Exploring Reflections in the Plane Continued
- LESSON 6: Reflections in the Coordinate Plane Continued Again - finishing it up
- LESSON 7: Exploring Rotations in the Plane
- LESSON 8: Exploring Rotations in the Plane Extension Activity
- LESSON 9: Exploring Rotations in the Plane Extension Activity Continued
- LESSON 10: Exploring Rotations in the Plane Extension Activity Completed
- LESSON 11: Rotations in the Coordinate Plane
- LESSON 12: Combining Transformations Formative Assessment Lesson
- LESSON 13: Combining Transformations Formative Assessment Lesson Continued
- LESSON 14: Combining Transformations Formative Assessment Lesson Completed
- LESSON 15: Exploring Angle Relationships Through Transformations
- LESSON 16: Exploring Angle Relationships Through Transformaitons Continued
- LESSON 17: Exploring Angle Relationships Along Parallel Lines
- LESSON 18: Angle Relationships Along Parallel Lines Continued
- LESSON 19: Angle Relationships Along Parallel Lines Completed
- LESSON 20: Optional Parallel Lines Unit Project Day 1 of 2
- LESSON 21: Optional Parallel Lines Unit Project Day 2 of 2
- LESSON 22: Transformations Unit Exam
- LESSON 23: Parallel Lines Challenge Problem