$$
\begin{aligned}
& \mathrm{L}_1: x-y=0 \\
& \mathrm{~L}_2: x+2 y=3 \\
& \mathrm{~L}_3: x+y=6
\end{aligned}
$$
on solving $\mathrm{L}_1$ and $\mathrm{L}_2$ :
$y=L$ and $x=1$
$\mathrm{L}_1$ and $\mathrm{L}_3$ :
$$
\begin{aligned}
& x=2 \\
& y=2
\end{aligned}
$$
$\mathrm{L}_2$ and $\mathrm{L}_{3 \text { ain }}$.
$$
\begin{aligned}
& x+y=3 \\
& 2 x+y=6 \\
& x=3 \\
& y=0 \\
& A C=\sqrt{4+1}=\sqrt{5} \\
& B C=\sqrt{4+1}=\sqrt{5} \\
& A B=\sqrt{1+1}=\sqrt{2}
\end{aligned}
$$
sa its an isosceles triangle