Which of the following was common among all Native American groups in North America at the beginning of European colonization?

The answer that describes a commonality among all Native American groups in North America at the beginning of European colonization is that they all relied primarily on their own feet for transportation. This reflects the understanding that many Indigenous peoples utilized walking as their main means of travel, given the lack of developed infrastructure for mechanized transportation.

While some groups did create advanced systems of travel such as canoes for waterways or sleds and travois for carrying goods, the reliance on walking as a fundamental form of transportation is broadly applicable to various tribes, especially in the context of their nomadic or semi-nomadic lifestyles prior to European influence and the introduction of horses and other modes of transport.

The other choices present characteristics that do not universally apply to all Native American groups. Not all tribes were nomadic; many established settled communities with agriculture. The organizational structures of government and religion varied widely among different tribes, so it's not accurate to say all had highly organized systems. Additionally, social structures differed significantly, with some tribes practicing matrilineal systems, where lineage and inheritance were traced through mothers rather than fathers. Therefore, the statement about relying on their own feet for transportation captures a fundamental aspect of the way of life common among many Native American groups before the arrival of