Final answer:
The chordae tendineae are the string-like structures that attach the flaps of the atrioventricular valves to the heart's papillary muscles, preventing inversion and ensuring proper blood flow.
Step-by-step explanation:
The string-like structures that anchor the valve flaps of the atrioventricular (AV) valves, specifically the tricuspid valve in the right side of the heart and the mitral valve in the left side of the heart, are known as the chordae tendineae. These heart strings play a crucial role in the function of the AV valves by connecting the valve flaps to papillary muscles on the walls of the heart's ventricles. As the heart contracts, these muscles exert tension on the chordae tendineae, preventing the valves from inverting and ensuring that blood flows only in the correct direction through the heart.