True. All isosceles triangles with a 40 degree vertex angle are similar because the corresponding angles are all equal, each triangle having angles of 40-70-70.
An isosceles triangle is a triangle with (at least) two equal sides. It has both two equal sides and two equal angles. The name derives from the Greek iso (same) and skelos (leg).
A triangle with all sides equal is called an equilateral triangle, and a triangle with no sides equal is called a scalene triangle.
An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides and angles equal. Another special case of an isosceles triangle is the isosceles right triangle.
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