When sarah was 6 months old, she was 21 inches tall and her head had a diameter of 4.5 inches. now, at 20 year sold, she is 6 ft 1 in. tall and her head has a diameter of 7.65 inches. if sarah is typical, should a person at 20 years of age be considered "similar" to herself at 6 months of age?

Yes, she could be considered similar to herself at 6 months of age.

In mathematics, the concept of similarity is about proportion relationships. In this problem, we are discussing the relationships between age, height and diameter. We are not discussing the absolute value of the numbers themselves.

For example in Geometry, a very small triangle can be similar to a very large triangle if all the angles of the triangle are congruent. The size doesn't matter.