Final answer:
Active Directory Domains and Trusts is used to verify the parent-child trust relationship between domains.
Step-by-step explanation:
The tool that can be used to verify the parent-child trust relationship following the installation of a new child domain in an existing Active Directory Domain network is Active Directory Domains and Trusts. This tool allows you to manage trust relationships between domains in an Active Directory environment. By accessing the properties of the new child domain, you can verify and configure the trust relationship with the parent domain.
While Active Directory Sites and Services, Active Directory Users and Computers, and Computer Management are all important tools for managing various aspects of Active Directory, they do not specifically deal with verifying trust relationships between domains.