Question

1. for which of these shapes is it possible to apply the pythagorean theorem directly? a. right triangle b. circle c. square d. equilateral triangle

Explanation:

The Pythagorean Theorem ($a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the legs of a right - triangle and $c$ is the hypotenuse) is specifically formulated for right - triangles. A circle has properties related to radius, diameter, circumference ($C = 2\pi r$) and area ($A=\pi r^{2}$). A square has side - length relationships for perimeter ($P = 4s$) and area ($A=s^{2}$). An equilateral triangle has all sides equal and uses formulas like the area formula $A=\frac{\sqrt{3}}{4}a^{2}$ (where $a$ is the side - length). Only the right - triangle's side lengths directly follow the Pythagorean Theorem.

Answer:

A. Right triangle