The simplest example I can think of is a square and a rectangle: they both have 4 right angles, but they are not similar: the sides of a square are all the same length, the sides of a rectangle aren't.
So, there's no way you can start with a square and end with a rectangle by rotating/translating/dilating the shape. You'll need to squeeze the square along one direction only to get a square.
This means that the two shapes are not similar, even if they have the same angles.
