Final answer:
No, if the Moon rotated at the same rate as Earth, we would not always see the same side. The Moon's current synchronous rotation is the reason why we always see the same side from Earth.
Step-by-step explanation:
If the Moon rotated on its axis just as fast as the Earth, the question is, would we still see the same side of the Moon from Earth? The answer is no, we would not. The reason for this is that the Moon currently rotates on its axis in the exact same amount of time that it takes to orbit the Earth, a phenomenon known as synchronous rotation.
This synchronous rotation is what keeps the same hemisphere of the Moon facing Earth at all times. If the Moon were to rotate at a pace different from its orbital period, then similar to Earth's rotation, we would see different sides of the Moon as it orbited Earth. This concept can be visualized by imagining a scenario where a person has an arrow stuck into them and as they walk around another person, they also rotate so that the arrow always points at the person in the middle. This mimics the Moon's current synchronous rotation.