Final answer:
The discovery of written records, specifically oracle bones inscribed with Chinese characters, convinced scholars that the Shang dynasty was not a mythical dynasty.
Step-by-step explanation:
The key piece of evidence that convinced scholars that the Shang dynasty was not a mythical dynasty, as was once believed, is the discovery of written records. Specifically, the discovery of old turtle shells inscribed with Chinese characters in a medicine shop, known as oracle bones, provided written records from China's first dynasty. These oracle bones, once used in the art of divination, were recognized as primary texts from the Shang period and proved the existence of the Shang dynasty.