CCSS.Math.Content.8.G.B.7
The standard
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Common Core State Standards for Mathematics · Geometry
What this standard means
Students need to use the Pythagorean Theorem to find a missing side in a right triangle, including word problems, coordinate grids, and 3D figures. They must identify the right angle, choose the legs and hypotenuse, substitute correctly, and solve for the unknown length.
Mastery looks like setting up a² + b² = c² without guessing, using square roots correctly, and labeling answers with units. Students often mix up the hypotenuse, forget to square both legs, or use the theorem on triangles that are not right triangles.
Ways to teach it
- Have students measure two perpendicular sides of a taped floor triangle, then calculate and check the diagonal with a tape measure.
- Ask students to explain how they know which side is the hypotenuse before solving a missing-side problem.
- Give a three-question exit ticket: find a leg, find a hypotenuse, and solve one 3D diagonal problem.
- Use a ladder-against-a-wall or TV-size problem to connect side lengths, diagonals, and square roots.
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