The goal of this discussion is for students to work toward a more convincing proof. Use Stronger and Clearer Each Time to give students an opportunity to revise and refine their proof that for any acute angle . In this structured pairing strategy, students bring their first draft response into conversations with 2–3 different partners. They take turns being the speaker and the listener. As the speaker, students share their initial ideas and read their first draft. As the listener, students ask questions and give feedback that will help clarify and strengthen their partner’s ideas and writing.

Display these prompts for feedback:

• “ makes sense, but what do you mean when you say ?”
• “How do you know ? What else do you know is true?”
• Can you use the diagram to show ?

Close the partner conversations, and give students 3–5 minutes to revise their first draft. Encourage students to incorporate any good ideas and words they got from their partners to make their next draft stronger and clearer.

After Stronger and Clearer Each Time, tell students that while this theorem won’t be added to the reference chart, it will be useful for the next activity.

The goal is to discuss the first question. Invite students to share their reasoning for this question.

Display several similar right triangles with one angle labeled theta, and ask students to supply side lengths that would result in .