a. The complementary base of adenine (A) is thymine (T). b. The complementary base of thymine (T) is adenine (A). c. The complementary base of cytosine (C) is guanine (G). d. The complementary base of guanine \((G)\) is cytosine (C).

The intricate structure of DNA is a marvel of biological engineering, featuring a double-helix configuration that resembles a twisted ladder. It is composed of four different types of nucleotides, which are the basic building blocks of DNA. Each nucleotide consists of a sugar molecule, a phosphate group, and a nitrogenous base.

There are two strands in the DNA double-helix, and these strands are held together by the chemical bonding of nitrogenous bases from opposing strands. The sequence of these bases along the DNA strand is what encodes genetic information. The arrangement and stability of the DNA structure facilitate accurate replication during cell division, ensuring genetic fidelity across generations.

To further elaborate, the sugar component of each nucleotide is deoxyribose, which is why DNA is referred to as deoxyribonucleic acid. The phosphate groups link between sugars of two adjacent nucleotides, creating a 'backbone' for each single DNA strand. It's the nitrogenous bases, however, that play the starring role in establishing the characteristic double helix.

In the world of genetics, adenine (A) and thymine (T) are like perfect dance partners, always finding each other amidst the crowd. The rationale for their specific pairing is rooted in their molecular structures; adenine, a purine base with a double-ring structure, pairs with thymine, a pyrimidine base with a single-ring structure.

Adenine and thymine are attracted to each other due to hydrogen bonding, where adenine has two hydrogen bonding sites that neatly fit with the two available sites on thymine. It's this precise interaction that allows for the consistent 'AT' pairing along the DNA strand. In every organism, wherever there is an 'A' on one strand, a matching 'T' is found on the opposing strand, like a rule that nature never breaks. This pairing is crucial for the DNA’s double-helical structure and for maintaining the integrity of the genetic code during processes like replication and transcription.

Just as adenine finds its match in thymine, cytosine (C) and guanine (G) are the other indispensable pair in DNA. Cytosine, a pyrimidine base with a single ring structure, forms a strong bond with guanine, a purine base with a complementary double ring structure.

Cytosine and guanine have a bonding pattern that involves three hydrogen bonds, which is one more than adenine and thymine’s two hydrogen bonds. This additional bond gives the CG pairing a slightly stronger attachment, and this increased stability plays a part in the overall resilience of the DNA molecule. Their bond ensures that for every 'C' on one DNA strand, there is a 'G' to meet it on the other strand, following the strict rules of the genetic code. The fidelity of cytosine and guanine pairing is a cornerstone for replicating DNA accurately, an action that is fundamental to life as we know it.