No, not all isosceles triangles are similar. While all isosceles triangles share the property of having at least two sides of equal length, the angles can vary between different isosceles triangles.
Similarity in triangles is determined by the angles. If two triangles have the same shape, meaning their corresponding angles are equal, they are similar. In the case of isosceles triangles, the angles opposite the equal sides are the same, but the vertex angle can differ. This means you can have isosceles triangles with different angles and therefore different shapes.
For example, one isosceles triangle might have angles of 70°, 70°, and 40°, while another might have angles of 50°, 50°, and 80°. Because these angle measures are not the same, the triangles are not similar, even though both are isosceles.
In summary, while all isosceles triangles have two equal sides, they are not all similar due to the potential differences in the angles between them.