Step 1: Understanding evolutionary relationship determination.
Mitochondrial DNA (mtDNA) is often used to determine the evolutionary relationships of species because it is inherited maternally and accumulates mutations more rapidly than nuclear DNA, making it a good marker for tracing evolutionary history.
Step 2: Analyzing the options.
- (A) the size of their nuclei: Nucleus size varies significantly among species but is not as reliable for evolutionary relationship determination.
- (B) the size of their Golgi bodies: Golgi body size is also not a primary factor for evolutionary relationship determination.
- (C) their mitochondrial DNA sequences: mtDNA is the best choice for studying evolutionary relationships, as it evolves faster and is maternally inherited, making it highly useful for phylogenetic analysis.
- (D) the number of mitochondria in their cells: The number of mitochondria varies based on energy needs but does not serve as a good marker for evolutionary relationships.
Final Answer: \[ \boxed{\text{(C) their mitochondrial DNA sequences.}} \]