the diagram below shows DNA molecules. What do the broken lines connected to hydrogen atoms represent in this diagram?

Answer is: hydrogen bonds.

Hydrogen bond is an electrostatic attraction between two polar groups that occurs when a hydrogen atom (H), covalently bound to a highly electronegative atom such as flourine (F), oxygen (O) and nitrogen (N) atoms.

According to the principle of base pairing hydrogen bonds could form between adenine and thymine (two hydrogen bonds between this nucleobases) and guanine and cytosine (three hydrogen bonds between this nucleobases).

Adenine and guanine are purine derivatives and thymine and cytosine are pyrimidine derivates.