The purpose of this activity is for students to identify the hypotenuse in right triangles in different orientations.

The goal of this discussion is to make sure students understand that only right triangles have a hypotenuse, and that in a right triangle the hypotenuse is always the side opposite the right angle.

Here are some questions for discussion:

• “In a right triangle, does it matter which side is and which is ?” ( and must be the two shorter sides of the right triangle, but it does not matter which side is or .)
• “How do you know the side you selected is the hypotenuse?” (It is the longest side. It is the side opposite the right angle.)
• “Why does Triangle B not have a hypotenuse?” (It is not a right triangle.)

The purpose of this activity is to give students practice finding unknown side lengths in a right triangle using the Pythagorean Theorem.

The purpose of this discussion is for students to share how they calculated the unknown side lengths. Ask students to share their answers and reasoning for the first two questions. For the third question with sides of length 2.4 cm and 6.5 cm, display any triangles students drew for all to see, noting any differences. For example, students may have drawn triangles with different orientations or labeled different sides as and .

Then use Critique, Correct, Clarify to give students an opportunity to improve a sample written response for finding the unknown side length for the triangle with known side length and hypotenuse by correcting errors, clarifying meaning, and adding details. 

• Draw a right triangle with legs labeled and . Then display this first draft next to it: “I know that and , so when I use the Pythagorean Theorem, I get the equation .”

• Ask, “What parts of this response are unclear, incorrect, or incomplete?” As students respond, annotate the display with 2–3 ideas to indicate the parts of the writing that could use improvement.

• Give students 2–4 minutes to work with a partner to revise the first draft. 

• Select 1–2 individuals or groups to read their revised draft aloud slowly enough to record for all to see. Scribe as each student shares, then invite the whole class to contribute additional language and edits to make the final draft even more clear and more convincing.

Point out that when two sides of a right triangle are known, the third can always be found by using the Pythagorean Theorem. Remind students it is important to keep track of which side is the hypotenuse.