Which of the following is considered a deep ball-and-socket joint in dogs and cats?

The hip joint is considered a deep ball-and-socket joint in dogs and cats due to its anatomical structure that allows for a wide range of motion. In a ball-and-socket joint, a spherical head of one bone fits into a cup-like cavity of another bone, which is precisely what occurs in the hip joint. This design enables the joint to facilitate movements such as flexion, extension, abduction, and rotation, making it crucial for activities such as walking, running, and jumping.

The depth of the socket in the hip joint provides stability while still allowing for the flexibility necessary for the animal's mobility. This is contrasted with the shoulder joint, which, although also a ball-and-socket joint, is a shallower articulation that provides a greater range of motion but less stability. On the other hand, the elbow and knee joints are hinge joints, primarily allowing movement in one direction rather than the multi-directional movement typical of ball-and-socket joints. Thus, the hip joint stands out as the primary example of a deep ball-and-socket joint in these animals.