Final answer:
During an autogenic inhibition stretch of the quadriceps, the hamstrings are the antagonistic muscles that contract and relax to allow for an effective stretch.
Step-by-step explanation:
When an autogenic inhibition stretch of the quadriceps muscle occurs, it is the antagonist muscles, specifically the hamstrings, that need to relax and contract. This process is a result of autogenic inhibition, which involves the muscle spindle within the quadriceps sending a signal to inhibit the motor neurons of the antagonistic muscles, in this case, the hamstrings.
This inhibition allows for a more effective stretch of the quadriceps by limiting the contraction of the opposing muscles, thus aiding in muscle relaxation and lengthening.