Final answer:
The statement is true; centrosomes in animal cells are microtubule-organizing centers that do indeed contain centrioles, which are essential for organizing microtubules and facilitating cell division.
Step-by-step explanation:
The centrosome is a critical component of animal cells, functioning as the main microtubule-organizing center. This structure is located near the nucleus and plays a pivotal role in organizing the microtubules that are essential for cell shape, organization, and division. Each centrosome contains a pair of centrioles, which are characterized by their cylindrical shape, consisting of nine triplets of microtubules arranged perpendicularly to each other. The centrioles are crucial for the proper organization and segregation of chromosomes during cell division, as they participate in spindle fiber formation during mitosis. This makes centrosomes and centrioles vital to the cell's structural integrity and reproductive processes.
In conclusion, the presence of centrioles within the centrosome, their functionality as a microtubule organizing center, and their involvement in cell division underpin the accuracy of the statement that centrosomes contain centrioles and serve as microtubule-organizing centers in animal cells.