Final answer:
The femoral artery and vein, which serve the lower limbs, pass through the thigh and transform into the popliteal artery and vein posterior to the knee before reaching the popliteal fossa.
Step-by-step explanation:
The femoral artery is a continuation of the external iliac artery after it exits the body cavity. As it travels through the thigh, it gives rise to several branches including the lateral deep femoral artery and the genicular artery. The femoral artery then transitions into the popliteal artery as it passes posterior to the knee, eventually reaching the popliteal fossa. Meanwhile, the femoral vein, which drains the upper leg, receives blood from various tributaries such as the great saphenous vein and becomes the external iliac vein as it crosses the body wall into the body cavity. The vascular supply of the lower limbs is crucial for the delivery of oxygen and nutrients as well as the removal of waste products from the leg tissues.