Students continue to practice drawing triangles from given conditions and categorizing their results. This activity focuses on the inclusion of a single angle and two sides. Again, they do not need to memorize which conditions result in unique triangles, but they should begin to notice how some conditions (such as the equal side lengths) result in certain requirements for the completed triangle.

When students articulate their reasoning, they have an opportunity to attend to precision in the language they use to describe their thinking (MP6). They might first propose less formal or imprecise language, and after sharing with a partner, revise their explanation to be clearer and stronger. 

There is an optional blackline master that can help students organize their work.

Use Stronger and Clearer Each Time to give students an opportunity to revise and refine their response to “Did either of these sets of measurements determine one unique triangle? How do you know?” 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 their partner clarify and strengthen their ideas and writing.
If time allows, display these prompts for feedback: 

• “ makes sense, but what do you mean when you say. . . ?”
• “Can you describe that another way?”
• “How do you know . . . ? What else do you know is true?”

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

If the optional blackline master was used, ask students:

• “Which configurations made identical triangles?” (the top left and bottom left)
• “Which configurations made more than one triangle?” (the bottom right)

If not mentioned by students, explain to students that the top left and bottom left configurations result in the same triangle, because in both cases the angle is in between the 4-cm and 5-cm sides, and that the bottom right configuration results in two different triangles, because the arc intersects the ray in two different places.

This activity focuses on including three angle conditions. The goal is for students to notice that some angle conditions result in a large number of possible triangles (all scaled copies of one another) or are impossible to create. Students are not expected to learn that the angle measures in a triangle must have a sum of 180 degrees, but they are not barred from noticing this fact.