Final answer:
The statement is true; the Aztecs entered the valley of Mexico in 1325 and established Tenochtitlán. Prior to their arrival, the Toltecs dominated the area, and the Aztecs rose to prominence after the Toltech decline. The Aztec Empire eventually fell due to a combination of Spanish conquest and alliances with local indigenous groups.
Step-by-step explanation:
The statement that the Aztecs entered the valley of Mexico in 1325 is true. The Aztecs, known as the Mexica, were a nomadic tribe that emerged in the Valley of Mexico as a dominant force after a period of migration. Their eventual settlement is notably marked by the foundation of the city of Tenochtitlán on an island in Lake Texcoco, fulfilling a prophecy of their chief god, Huitzilopochtli.
Prior to the rise of the Mexica, several societies had left their mark on the Valley of Mexico. Notably, the Toltecs, who held sway from their capital at Tula from about the 10th to the 12th century CE, created a significant cultural and political vacuum when their rule collapsed. The Aztecs excelled in the unrest that followed, becoming valued as mercenaries before finding their place on the islands of Lake Texcoco.
As the Aztecs established their capital, they developed a reputation as fierce warriors and within a few centuries, they forged an Empire by exerting dominance over other city-states in the region. However, this era of Aztec ascendancy came to an end with the arrival of the Spanish, led by Hernán Cortés. The arrival of the Europeans sparked new conflicts and ignited existing resentments among indigenous groups against Aztec rule, such as the Tlaxcalan, which ultimately contributed to the fall of the Aztec Empire.