Final answer:
The common action of muscles in the medial compartment of the thigh is adduction of the femur, while the common action of muscles in the lateral compartment is extension of the knee.
Step-by-step explanation:
The medial compartment of the thigh includes the adductors, pectineus, and the gracilis. These muscles are responsible for adducting the femur at the hip, which means they bring the thigh towards the midline of the body. For example, when you squeeze your legs together, you are using the muscles in the medial compartment of the thigh.
The lateral compartment of the thigh is comprised of the quadriceps femoris, specifically the vastus lateralis muscle. This muscle is responsible for extending the knee. When you kick your leg forward, the vastus lateralis is one of the muscles that helps to straighten the knee.