Final answer:
The property manager's action to relocate the family without consulting the owner is valid under an agency relationship that involves actual or emergency authority, which is typically included in managerial responsibilities.
Step-by-step explanation:
The action taken by the property manager can be held as valid under an agency relationship known as actual authority or emergency authority. This authority implies that the manager has the power to make decisions on behalf of the property owner in situations where immediate action is necessary, such as relocating a family due to an unlivable apartment caused by a storm. In cases where the property is damaged, and the residents need to be rehoused immediately, the manager's ability to act without direct consultation with the owner is typically granted as a part of their managerial responsibilities.