MA.8.GR.1.1 MA.8.GR.1.2 MA.8.GR.1.3 Math.8.G.7 8.G.B.7 Math.8.G.8 8.G.B.8 CC.2.3.8.A.3 M08.C-G.2.1.1 M08.C-G.2.1.2 M08.C-G.2.1.3

Common Core Standards Pythagorean Theorem
Grade:	8th Grade
Standard:	MA.8.GR.1.1
Description:	Apply the Pythagorean Theorem to solve mathematical and real-world problems involving unknown side lengths in right triangles.
Standard:	MA.8.GR.1.2
Description:	Apply the Pythagorean Theorem to solve mathematical and real-world problems involving the distance between two points in a coordinate plane.
Standard:	MA.8.GR.1.3
Description:	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.
Standard:	Math.8.G.7 or 8.G.B.7
Description:	Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Standard:	Math.8.G.8 or 8.G.B.8
Description:	Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Standard:	CC.2.3.8.A.3
Description:	Understand and apply the Pythagorean Theorem to solve problems.
Standard:	M08.C-G.2.1.1
Description:	Apply the converse of the Pythagorean theorem to show a triangle is a right triangle.
Standard:	M08.C-G.2.1.2
Description:	Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Standard:	M08.C-G.2.1.3
Description:	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}

Common Core Standards