Geometry: Explaining and Applying the Pythagorean Theorem (CCSS.8.G.6) Practice Test

On a coordinate plane, the horizontal and vertical differences between two points form the legs of a right triangle. By the Pythagorean Theorem, if the legs have lengths $a$ and $b$, then the distance $c$ between the points satisfies $a^2+b^2=c^2$. Conversely, if $a^2+b^2=c^2$, the triangle is right because the legs are perpendicular.

On a coordinate grid, the run and rise between two points are perpendicular, forming a right triangle. The distance is the hypotenuse $c$ with $c^2=a^2+b^2$. Conversely, if $a^2+b^2=c^2$, the triangle is right.