Why do two normal distributions that have equal standard deviations have the same shape?

Step 1 
The reason why two normal distributions with equal standard deviations have the same shape in this situation must be explained.
Step 2 
The standard deviation is the square root of departures from the mean, and the normal distributions were bell-shaped or symmetric about the population mean. That is, spread from the mean. Thus, two normal distribution with equal standard deviation have same shape.