Final answer:
The anterior and posterior tibial arteries, which are continuations of the femoral artery, are at risk during tibial tubercle avulsion fractures due to their proximity to the tibial tuberosity, the site of the patellar tendon attachment.
Step-by-step explanation:
The vessel that is at risk with tibial tubercle avulsion fractures is the continuation of the femoral artery which branches into the anterior and posterior tibial arteries posterior to the knee. The tibial tuberosity, where avulsion fractures commonly occur, is located on the anterior side of the proximal tibia and is the site of attachment for the patellar tendon. Such fractures can result in damage to the nearby vascular structures, specifically the arteries that traverse the knee area to supply the lower leg.