Final answer:
The muscles that anchor the atrioventricular valves to chordae tendineae in the ventricles are the papillary muscles. They contract with the ventricles to prevent valve flaps from being pushed back and permit proper blood flow direction.
Step-by-step explanation:
The muscles present in the ventricles that anchor the atrioventricular valves by tendon-like chords called chordae tendineae are the papillary muscles. These muscles are extensions of the myocardium of the ventricles and are essential in preventing the backflow of blood into the atria during ventricular contraction. When the ventricles contract, the papillary muscles also contract, creating tension on the chordae tendineae and preventing the flaps of the valves from being forced back into the atria.
The right ventricle, for instance, has three papillary muscles named the anterior, posterior, and septal muscles. In contrast, the semilunar valves, such as the aortic and pulmonary valves, do not have these chordae tendineae or papillary muscles. Instead, they are sealed by blood pressing against their cusps when the ventricles relax.