Official solution
The given three lines are x - y = 0, x + 2y = 3 and 2x + y = 6 then point of intersection,
lines x - y = 0 and x + 2y = 3 is (1, 1)
lines x - y = 0 and 2x + y = 6 is (2, 2)
and lines x + 2y = 3 and 2x + y = 0 is (3, 0)
The triangle ABC has vertices A(1, 1), B(2, 2) and C(3, 0)
\[ \therefore \] AB = \[\sqrt 2 \], BC = \[\sqrt 5 \] and AC = \[\sqrt 5 \]
\[ \therefore \] \[\Delta\]ABC is isosceles