Answer
Yes
Work Step by Step
Points are $(2,6)$, $(0, -2)$, and $(5,1)$
Distance between $(2,6)$ and $(0,-2)$
$\sqrt {(6- -2)^2 + (2-0)^2}$
$\sqrt {(8^2 + 2^2)}$
$\sqrt {64+4}$
$\sqrt {68}$
Distance between $(2,6)$ and $(5,1)$
$\sqrt {(6-1)^2 + (5-2)^2}$
$\sqrt {5^2 + 3^2}$
$\sqrt {25 + 9}$
$\sqrt {34}$
Distance between $(0,-2)$ and $(5,1)$
$\sqrt {(5-0)^2 + (1- -2)^2}$
$\sqrt {5^2 + 3^2}$
$\sqrt {25+9}$
$\sqrt {34}$
The distance of two line segments of the triangle are the same. Thus, the triangle is isosceles.
