This Warm-up prompts students to compare four images. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another. In particular, students will be focused on the characteristics of perpendicular lines.

Ask each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations, and ensure the reasons given are correct.

During the discussion, ask students to explain the meaning of any terminology they use, such as “perpendicular.” Also, press students on unsubstantiated claims.

Math Community

After the Warm-up, display the Math Community Chart and a list of 2–5 revisions suggested by the class in the previous exercise for all to see. Remind students that norms are agreements that everyone in the class shares responsibility for, so everyone needs to understand and agree to work on upholding the norms. Briefly discuss any revisions and make changes to the “Norms” sections of the chart as the class agrees. Depending on the level of agreement or disagreement, it may not be possible to discuss all suggested revisions at this time. If that happens, plan to discuss the remaining suggestions over the next few lessons.

Tell students that the class now has an initial list of norms or “hopes” for how the classroom math community will work together throughout the school year. This list is just a start, and over the year it will be revised and improved as students in the class learn more about each other and about themselves as math learners.

The proof that if a point is the same distance from as it is from , then must be on the perpendicular bisector of is challenging. Students may struggle to make sense of what it means to prove that a point must be on a line. This proof, like the proof of the Isosceles Triangle Theorem, requires thinking carefully about how to define an auxiliary line. In this activity students critique the reasoning of others before attempting to write a proof on their own. A copy of the script is provided with the blackline masters for this lesson.

Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5).

In a previous activity, students had a chance to practice giving feedback on proofs. In this activity, they will put their proof-writing and feedback-giving skills to work as they draft proofs and then give feedback to a partner. Students have already drawn diagrams of this situation in an earlier lesson, so the focus of this activity is writing a proof that is clear and easy to understand (MP3). Students will make revisions to the proofs they write in the Cool-down, so focus discussion on common concerns.

Making dynamic geometry software available gives students an opportunity to choose appropriate tools strategically (MP5).