Final answer:
The 'sons' of an isosceles triangle that 'changed their shapes' could metaphorically refer to becoming an equilateral, scalene, or right-angle triangle, with potential nicknames like 'Perfect Triangle' for the equilateral due to its symmetrical properties.
Step-by-step explanation:
The question appears to be in the context of geometry but is phrased in a metaphorical and literary manner. Typically, shape transformations in geometry don't involve 'surgery', but rather changing angles and lengths. However, using this metaphorical language, we could imagine that the 'sons' of an isosceles triangle who 'changed their shapes' could be referring to transformations such as becoming a different type of triangle, such as equilateral, scalene or right angle triangle. Each of these triangles has different attributes.
For example an equilateral triangle has three sides of equal length and three equal angles, each measuring 60 degrees. A scalene triangle has no sides of equal length and no equal angles. Lastly a right-angle triangle has one 90-degree angle. These 'sons' can earn various nicknames based on their properties, such as 'Equilateral' being nicknamed the 'Perfect Triangle' due to its symmetrical nature.