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# Flow Proofs and PTA

Lesson 5 of 9

## Objective: SWBAT write flow proofs and use that angles formed by a transversal can prove that lines are parallel.

#### Do Now

*10 min*

Students will find missing angle measurements based on theorems relating to parallel lines, transversals and angles like alternate interior, alternate exterior and consecutive interior. This helps to reinforce precision when using vocabularly for this unit (MP 6) and also will help to remind students to relationships that have already been demonstrated in class, which we will now prove!

#### Resources

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#### Pair-Share and Mazes

*8 min*

The pair-share provides an opportunity for students to talk about how a maze relates to a proof. In this a teacher explains the connection and how a maze has a beginning and ending (like our given and prove). A maze also can be solved many different ways, just like our proofs! This sets up our work with Flow Proofs and proof by contradiction later in the lesson.

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This from Khan Academy explains how to use a proof by contradiction to show that when corresponding angles are congruent, lines must be parallel.

I show this video directly to my students and then ask them to explain in their own words what they saw in the video. The visuals in the video are great, and most of my students respond that you can "see" why the corresponding angles are not congruent if the lines are not parallel. This videos helps students access mathematical practices like #3, where students have to construct viable arguments and critique others.

After reviewing the video with students, you will go through the remaining concepts in student notes (see More Key Theorems). I find that students catch onto these concepts easily because these concepts are built upon prior knowledge learned from the past lessons. There are 2 practice examples which can be taught directly to students.

*Student Notes - Flow Proofs and PTA*

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#### Activity/Homework

*10 min*

Students can work on the activity, which includes 2 proofs, in class or complete this assignment as homework. These proofs mirror examples that we have completed in class. Proofs can be challenging for students, and it can be hard to get them to start on their own. One suggestion is to ask students to have their student notes on their desk and try the proofs BEFORE asking you or a peer for help. I usually ask students to fill in one box before I give them a hint on a next step!

**Student Notes - PTA and Flow Proofs**

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#### Exit TIcket

*10 min*

Students will explain, in words, the similarities and differences between 2-column proofs and flow proofs. If you have enough time, this is a great Exit Ticket to review in-class with students and receive input on. You also can take a vote for which method students like best!

#### Resources

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- UNIT 1: Introduction to Geometry: Points, Lines, Planes, and Angles
- UNIT 2: Line-sanity!
- UNIT 3: Transformers and Transformations
- UNIT 4: Tremendous Triangles
- UNIT 5: Three Triangle Topics
- UNIT 6: Pretty Polygons
- UNIT 7: MidTerm Materials
- UNIT 8: Circles
- UNIT 9: 3-D Shapes and Volume
- UNIT 10: Sweet Similar Shapes
- UNIT 11: Trig Trickery
- UNIT 12: Finally Finals

- LESSON 1: Proving It
- LESSON 2: Prove It with Angle Relationships
- LESSON 3: Skew Lines and their Friends
- LESSON 4: PTA (Parallel Lines, Transversals and Angles)
- LESSON 5: Flow Proofs and PTA
- LESSON 6: Line It Up!
- LESSON 7: Perp Lines are Perfect
- LESSON 8: Parabolas and Review of Line-sanity!
- LESSON 9: Assessment for Line-Sanity