Final answer:
A plane that divides the body into right and left sides is called the sagittal plane, which can be specifically a midsagittal plane if it divides the body into equal halves.
Step-by-step explanation:
The plane described in your question is known as the sagittal plane. This plane divides the body or an organ vertically into right and left sides. If it runs exactly down the middle, creating two equal halves, it is termed the midsagittal or median plane. However, if the division results in unequal right and left sides, it is called a parasagittal plane or sometimes a longitudinal section. Another related plane is the frontal (or coronal) plane, which divides the body into anterior (front) and posterior (rear) sections, and the transverse (or horizontal) plane, which separates the body into upper and lower portions.