Answer
False
Work Step by Step
For any two isosceles triangles to be similar, the vertex angles of the two triangles need to be congruent.
For example: I could have one isosceles triangle with angle measures of $80^{\circ}, 50^{\circ}, 50^{\circ}$, and one isosceles triangle with angle measures of $90^{\circ}, 45^{\circ}, 45^{\circ}$. These two isosceles triangles are NOT similar.
