Which characteristic of dna allows each strand of the molecule to act as a template that specifies the exact sequence of nucleotides in the other strand?

The correspondency of the bases.

Explanation:

This is really important because it also allowed the scientist that first identified the DNA as the molecule that carries the genetic information. The correspondency of the bases means that each base only pairs with another specific one (Adenine with thymine and Cytosine with Guanine) meaning that when the strands are separated the same information will be contained in each strand. Therefore, when the new DNA is formed, it will be completely the same as the original because of this property.