Answer
$|PQ|=3$
$|QR|=3\sqrt{5}$
$|RP|=6$
The triangle is not isosceles.
Work Step by Step
The side lengths can be calculated using the distance formula:
$d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2+(z_{2}-z_{1})^2)}$
$|PQ|=\sqrt{(4-2)^2+(1+1)^2+(1-0)^2)}=3$
$|QR|=\sqrt{(4-4)^2+(-5-1)^2+(4-1)^2)}=\sqrt{45}=3\sqrt{5}$
$|RP|=\sqrt{(2-4)^2+(-1+5)^2+(0-4)^2)}=6$
Since none of the legs are the same length, the triangle is not isosceles.
