28 Math.8.G.7 8.G.B.7 8.GSR.8.2 8.G.7 8.G.B.5 27 Math.8.G.8 8.G.B.8 8.GSR.8.3 8.G.8 8.G.B.6 CC.2.3.8.A.3 M08.C-G.2.1.1 M08.C-G.2.1.2 M08.C-G.2.1.3 MA.8.GR.1.1 MA.8.GR.1.2 MA.8.GR.1.3 8.GSR.8.2 8.GSR.8.3 8.GM.3 8.GM.4 8.GM.5

Pythagorean Theorem 8th Grade

Alabama Course of Study Standards: 28
Apply the Pythagorean Theorem to determine unknown side lengths of right triangles, including real-world applications.
Common Core State Standards: Math.8.G.7 or 8.G.B.7
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Georgia Standards of Excellence (GSE): 8.GSR.8.2
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles within authentic, mathematical problems in two and three dimensions.
North Carolina - Standard Course of Study: 8.G.7
Apply the Pythagorean Theorem and its converse to solve real-world and mathematical problems.
Tennessee Academic Standards: 8.G.B.5
Know and apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Alabama Course of Study Standards: 27
Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane.
Common Core State Standards: Math.8.G.8 or 8.G.B.8 North Carolina - Standard Course of Study: 8.G.8 Tennessee Academic Standards: 8.G.B.6
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Georgia Standards of Excellence (GSE): 8.GSR.8.3
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system in practical, mathematical problems.
Pennsylvania Core Standards: CC.2.3.8.A.3
Understand and apply the Pythagorean Theorem to solve problems.
Pennsylvania Core Standards: M08.C-G.2.1.1
Apply the converse of the Pythagorean theorem to show a triangle is a right triangle.
Pennsylvania Core Standards: M08.C-G.2.1.2
Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Pennsylvania Core Standards: M08.C-G.2.1.3
Apply the Pythagorean theorem to find the distance between two points in a coordinate system.
Florida - Benchmarks for Excellent Student Thinking: MA.8.GR.1.1
Apply the Pythagorean Theorem to solve mathematical and real-world problems involving unknown side lengths in right triangles.
Florida - Benchmarks for Excellent Student Thinking: MA.8.GR.1.2
Apply the Pythagorean Theorem to solve mathematical and real-world problems involving the distance between two points in a coordinate plane.
Florida - Benchmarks for Excellent Student Thinking: MA.8.GR.1.3
Use the Triangle Inequality Theorem to determine if a triangle can be formed from a given set of sides. Use the converse of the Pythagorean Theorem to determine if a right triangle can be formed from a given set of sides.
Georgia Standards of Excellence (GSE): 8.GSR.8.2
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles within authentic, mathematical problems in two and three dimensions.
Georgia Standards of Excellence (GSE): 8.GSR.8.3
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system in practical, mathematical problems.
Arkansas Academic Standards: 8.GM.3
Model or explain an informal proof of the Pythagorean Theorem and its converse.
Arkansas Academic Standards: 8.GM.4
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles.
Arkansas Academic Standards: 8.GM.5
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Pythagorean Theorem

a^² + b^² = c^²

where a, b, and c are the side lengths of a right triangle,
and c is the length of the hypotenuse

\begin{array}{rcl} a^{2} + b^{2} & = & c^{2} \\ {(12 ft)}^{2} + b^{2} & = & {(20 ft)}^{2} \\ 144 {ft}^{2} + b^{2} & = & 400 {ft}^{2} \\ b^{2} & = & 256 {ft}^{2} \\ \sqrt{b^{2}} & = & \sqrt{256 {ft}^{2}} \\ b & = & 16 ft \end{array}

\begin{array}{rcl} a^{2} + b^{2} & = & c^{2} \\ 3^{2} + 4^{2} & = & c^{2} \\ 9 + 16 & = & c^{2} \\ 25 & = & c^{2} \\ \sqrt{25} & = & c \\ 5 & = & c \end{array}

Pythagorean Theorem

Alabama Course of Study Standards: 28

Apply the Pythagorean Theorem to determine unknown side lengths of right triangles, including real-world applications.

Common Core State Standards: Math.8.G.7 or 8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Georgia Standards of Excellence (GSE): 8.GSR.8.2

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles within authentic, mathematical problems in two and three dimensions.

North Carolina - Standard Course of Study: 8.G.7

Apply the Pythagorean Theorem and its converse to solve real-world and mathematical problems.

Tennessee Academic Standards: 8.G.B.5

Know and apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Alabama Course of Study Standards: 27

Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane.

Common Core State Standards: Math.8.G.8 or 8.G.B.8

North Carolina - Standard Course of Study: 8.G.8

Tennessee Academic Standards: 8.G.B.6

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Georgia Standards of Excellence (GSE): 8.GSR.8.3

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system in practical, mathematical problems.

Pennsylvania Core Standards: CC.2.3.8.A.3

Understand and apply the Pythagorean Theorem to solve problems.

Pennsylvania Core Standards: M08.C-G.2.1.1

Apply the converse of the Pythagorean theorem to show a triangle is a right triangle.

Pennsylvania Core Standards: M08.C-G.2.1.2

Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Pennsylvania Core Standards: M08.C-G.2.1.3

Apply the Pythagorean theorem to find the distance between two points in a coordinate system.

Florida - Benchmarks for Excellent Student Thinking: MA.8.GR.1.1

Apply the Pythagorean Theorem to solve mathematical and real-world problems involving unknown side lengths in right triangles.

Florida - Benchmarks for Excellent Student Thinking: MA.8.GR.1.2

Apply the Pythagorean Theorem to solve mathematical and real-world problems involving the distance between two points in a coordinate plane.

Florida - Benchmarks for Excellent Student Thinking: MA.8.GR.1.3

Use the Triangle Inequality Theorem to determine if a triangle can be formed from a given set of sides. Use the converse of the Pythagorean Theorem to determine if a right triangle can be formed from a given set of sides.

Georgia Standards of Excellence (GSE): 8.GSR.8.2

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles within authentic, mathematical problems in two and three dimensions.

Georgia Standards of Excellence (GSE): 8.GSR.8.3

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system in practical, mathematical problems.

Arkansas Academic Standards: 8.GM.3

Model or explain an informal proof of the Pythagorean Theorem and its converse.

Arkansas Academic Standards: 8.GM.4

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles.

Arkansas Academic Standards: 8.GM.5

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

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