Answer
See explanation.
Work Step by Step
The distance between two points: $\left(x_{1}, y_{1}, z_{1}\right)$ and $\left(x_{2}, y_{2}, z_{2}\right)$ is
\[
Distance=\sqrt{\left(y_{1}-y_{2}\right)^{2}+\left(z_{1}-z_{2}\right)^{2}+\left(x_{1}-x_{2}\right)^{2}}
\]
Distance between (1,7,3) and (4,5,2) is
\[
\sqrt{(-7+5)^{2}+(-3+2)^{2}+(-1+4)^{2}}=\sqrt{1+4+9}=\sqrt{14}
\]
Distance between (2,4,5) and (4,5,2) is
\[
\sqrt{(-4+5)^{2}+(-5+2)^{2}+(-2+4)^{2}}=\sqrt{9+1+4}=\sqrt{14}
\]
Distance between (2,4,5) and (1,7,3) is
\[
\sqrt{(-4+7)^{2}+(-5+3)^{2}+(-2+1)^{2}}=\sqrt{4+9+1}=\sqrt{14}
\]
Since the lengths of the three sides are equal, that is an equilateral triangle.
