Final answer:
The safe method to approach a downed deer or other large animal is to pause above and behind the animal's head to check for signs of breathing, ensuring personal safety.
Step-by-step explanation:
When approaching a downed deer or other large animal, you should pause above and behind the animal's head, and watch the chest cavity for any movement. This method ensures that you are not in the immediate path should the animal attempt to rise suddenly and allows you to observe for signs of breathing. Approaching from the front or making noise to startle the animal could be dangerous, and assuming the animal is safe because its eyes are closed is not reliable. Safety should always be the priority in these situations, so one must carefully observe the animal from a position that minimizes risk before proceeding.