In this lesson, students will learn how to identify if a triangle is a right triangle, or if certain lengths could create a right triangle. We’ll start by reviewing the pythagorean theorem to remind students that `a^2 + b^2` must equal `c^2`, before going into a “Can you make a right triangle?” Activity. Then students will practice identifying if a triangle would be a right triangle. You can expect this lesson with independent practice to take one `45`-minute class period.
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Students will be able to identify if side lengths could form a right triangle.
To start class, remind students what a right triangle looks like and what some of the key features are. You’ll want to share this slide with students and talk about the different vocabulary, while giving them time to write these key features down in their notebooks.
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Remind students of the Pythagorean theorem. It’s helpful as you’re explaining the formula to use the phrasing, “A triangle is a right triangle IF the sum of the squares of the two smaller side lengths is equal to the square of the longest side length”. Be sure to point out the parts of the equation you’re referring to as you explain it this way. This helps students start considering the concept of the converse of the Pythagorean Theorem without explicitly bringing up that vocabulary.
For this activity, students can work with a partner. Give each pair a copy of the Can you make a right triangle? Activity. (Be sure not to print these double-sided, as students will need to cut them!) There are different side lengths labeled with the measurements they represent from `2` units to `10` units. The idea is for students to test out combinations of `3` side lengths to see if they form a right triangle. They will first test out visually if they seem to form a right triangle, then they will use the converse of the Pythagorean theorem to check algebraically. This is a great activity for hands-on learners and gets all students engaged and thinking about what makes a right triangle, a right triangle!
After students have finished the activity, you’ll want to do a few example problems as a class. The slideshow contains three more problems to help students practice identifying if side lengths can form a right triangle.
Now it’s time for some independent practice! You can assign a ByteLearn online practice to your class using the link below. Students will get immediate feedback and step-by-step help if they need it. Set a due date and allow students to finish the assignment for homework. Once complete, you’ll see detailed reports of students who may need additional support, students who are ready for a challenge, and other interesting insights!
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