8.6.C 8.7.C 8.7.D

Pythagorean Theorem 8th Grade

Texas Essential Knowledge and Skills (TEKS): 8.6.C
use models and diagrams to explain the Pythagorean theorem.
Texas Essential Knowledge and Skills (TEKS): 8.7.C
use the Pythagorean Theorem and its converse to solve problems; and
Texas Essential Knowledge and Skills (TEKS): 8.7.D
determine the distance between two points on a coordinate plane using the Pythagorean Theorem.

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