Final answer:
The triceps brachii is the muscle that extends the elbow joint while doing pushups.
Step-by-step explanation:
The muscle that extends the elbow joint while doing pushups is the triceps brachii. The triceps brachii is a three-headed muscle located at the back of the upper arm and is responsible for straightening the elbow joint. When you are performing a push up, the triceps brachii contracts to extend the elbow and push your body away from the ground.