CCSS.Math.Content.8.G.B.6
The standard
Explain a proof of the Pythagorean Theorem and its converse.
Common Core State Standards for Mathematics · Geometry
What this standard means
Students need to explain why the Pythagorean Theorem works, not just use the formula. They should connect the side lengths of a right triangle to the areas of squares on those sides. They also need to explain the converse, if side lengths fit a² + b² = c², then the triangle is right.
Mastery looks like a student talking through a visual proof or rearrangement proof in their own words, with correct use of legs and hypotenuse. Common sticking points are mixing up c, treating any triangle as right, and memorizing steps without explaining why the areas match.
Ways to teach it
- Give pairs paper squares on triangle sides and have them cut, rearrange, and explain how the two smaller areas match the largest square.
- Prompt students: Explain to a younger student why a² + b² = c² only works for right triangles, using a diagram.
- Use an exit ticket with side lengths 6, 8, 10 and 5, 7, 9, asking which triangle is right and why.
- Show how a carpenter checks a square corner using a 3, 4, 5 triangle, then have students test a classroom corner.
Plan a lesson for CCSS.Math.Content.8.G.B.6
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Related standards
- CCSS.Math.Content.HSG-CO.C.10
Prove theorems about triangles.
- CCSS.Math.Content.8.G.B
Understand and apply the Pythagorean Theorem.
- CCSS.Math.Content.HSG-CO.C.11
Prove theorems about parallelograms.
- CCSS.Math.Content.HSG-SRT.B.4
Prove theorems about triangles.