This Warm-up prompts students to compare the graphs of four quadrilaterals. 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.

Invite each group to share one reason why a particular set of three go together. Record and display the responses. 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 that the reasons given are correct.

During the discussion, prompt students to explain the meaning of any terminology they use, such as “equilateral” or “diagonal,” and to clarify their reasoning, as needed. Consider asking:

• “How do you know _____?”
• “What do you mean by _____?”
• “Can you say that in another way?”

If possible, leave the list of responses displayed until the end of class. Students will return to these images during the Lesson Synthesis.

Students are presented with four points and are asked to fully describe the quadrilateral that has those points as its vertices. Slopes will show that all pairs of adjacent sides are perpendicular, making the shape a rectangle. Then students will use the Pythagorean Theorem to calculate both the area and the perimeter of the quadrilateral.

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

This activity gives students the opportunity to apply their work with distance and slope to triangles on the coordinate plane. The triangle in each figure uses the same coordinates for the longest side, allowing students to focus on the relationships between the smaller sides, including slope and side lengths. 

In this partner activity, students take turns deciding whether a triangle is a right triangle or not. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and to critique the reasoning of others (MP3).