Step 1: Understanding the Concept:
The endosymbiotic theory proposes that certain eukaryotic organelles evolved from free-living prokaryotic organisms that were engulfed by ancestral eukaryotic cells.
These organelles have retained structural and genetic features characteristic of their prokaryotic ancestors.
Step 2: Detailed Explanation:
Mitochondria and chloroplasts share several remarkable features with modern prokaryotic cells:
1. DNA: Both organelles contain their own genome, which consists of circular, double-stranded DNA lacking histone proteins, a feature typical of prokaryotes.
2. Ribosomes: They possess $70\text{S}$ ribosomes (composed of $50\text{S}$ and $30\text{S}$ subunits), which is the prokaryotic size, rather than the $80\text{S}$ ribosomes found in the eukaryotic cytoplasm.
3. Replication: They replicate independently within the cell through a process akin to binary fission, the division method of bacteria.
4. Membranes: They possess double membranes, where the inner membrane contains lipids like cardiolipin, which is characteristic of bacterial membranes.
In contrast, the nucleus (C) and Golgi apparatus (D) are strictly eukaryotic structures without endosymbiotic origins or prokaryotic features.
Step 3: Final Answer:
Therefore, only mitochondria and chloroplasts show similarity to prokaryotic cells, making option (A) the correct choice.