This Math Talk focuses on naming corresponding parts. It encourages students to think about which parts correspond and to rely on the structure of the figures to mentally solve problems. The understanding elicited here will be helpful later in the lesson when students use congruence statements in proofs.

In explaining their reasoning, students need to be precise in their word choice and use of language (MP6). 

To involve more students in the conversation, consider asking:

• “Who can restate ’s reasoning in a different way?”
• “Did anyone have the same strategy but would explain it differently?”
• “Did anyone solve the problem in a different way?”
• “Does anyone want to add on to ’s strategy?”
• “Do you agree or disagree? Why?”
• “What connections to previous problems do you see?”

If students disagree about triangles and , emphasize that yes, all the figures in the pictures are congruent, but we are asking about the figures named by the points. Invite a student to highlight for all to see the corresponding parts of triangles  and as named (use colored pencils to draw over segments  and in one color, segments  and in a second color, and segments  and  in a third color). Ask students if the corresponding parts as named are congruent.

Math Community

At the end of the Warm-up, display the Math Community Chart. Tell students that norms are expectations that help everyone in the room feel safe, comfortable, and productive doing math together. Using the Math Community Chart, offer an example of how the “Doing Math” actions can be used to create norms. For example, “In the last exercise, many of you said that our math community sounds like ‘sharing ideas.’ A norm that supports that is ‘We listen as others share their ideas.’ For a teacher norm, ‘questioning vs telling’ is very important to me, so a norm to support that is ‘Ask questions first to make sure I understand how someone is thinking.’”

Invite students to reflect on both individual and group actions. Ask, “As we work together in our mathematical community, what norms, or expectations, should we keep in mind?” Give 1–2 minutes of quiet think time and then invite as many students as time allows to share either their own norm suggestion or to “+1” another student’s suggestion. Record student thinking in the student and teacher “Norms” sections on the Math Community Chart. 

Conclude the discussion by telling students that what they made today is only a first draft of math community norms and that they can suggest other additions during the Cool-down. Throughout the year, students will revise, add, or remove norms based on those that are and are not supporting the community.

In a previous lesson, students justified that two figures being congruent guarantees that all pairs of corresponding parts are congruent. In this activity, students explore a different direction. If any pair of corresponding parts is not congruent, then the two figures cannot be congruent.

This activity previews the triangle congruence criteria. Here, they are given three pairs of congruent corresponding parts (two side lengths and one angle measurement), which is not enough information to be sure that all triangles with these measurements are congruent (this is an example of the Side-Side-Angle case).

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

The mathematical goal of this activity is to name corresponding parts, and recognize which parts correspond based on the congruence statement. The first figure is designed so students can see that the named angles do not correspond. The second figure is visually challenging, but the answer can be determined by looking at how the figures are named. The third figure has no diagram.

Monitor for students who see how to use the naming of figures to find the answer without a diagram.

This is the first time Math Language Routine 5: Co-Craft Questions is suggested in this course. In this routine, students are given a context or situation, often in the form of a problem stem (for example, a story, image, video, or graph) with or without numerical values. Students develop mathematical questions that can be asked about the situation. A typical prompt is: “What mathematical questions could you ask about this situation?” The purpose of this routine is to allow students to make sense of a context before feeling pressure to produce answers, and to develop students’ awareness of the language used in mathematics problems.