8.G.B.7 — Pythagorean Theorem

What 8.G.B.7 Covers

Grade 8, Geometry, Cluster B (understand and apply the Pythagorean Theorem). Students apply the Pythagorean Theorem to find unknown side lengths of right triangles in real-world and mathematical problems, in both two and three dimensions.

Where It Fits

Builds on Grade 8's informal proof of the Pythagorean Theorem and its converse (8.G.B.6). Leads into using the theorem to find distances between points on a coordinate plane, and later into high school geometry's trigonometric ratios. Often practiced alongside 6.G.A.1 and 8.G.C.9 as part of a Grade 6-8 geometry sequence.

Common Mistakes

• Adding the two legs directly instead of adding their squares before taking the square root.
• Mislabeling which side is the hypotenuse (it must be opposite the right angle).
• Forgetting the final square root step and leaving the answer as c².