Thank you for your advice.  The trigger ended up looking like this.

trigger DeletedAccountContactHistory on Account (before delete) {
List<Id>theIDs = new List<id>();
EntityHistory__c deletedRecord = new EntityHistory__c();
List <EntityHistory__c> listDeletedRecords = new List <EntityHistory__c>();

      for (Account theAccount:trigger.old)
      {
       //Build List of IDs
       theIDs.add(theAccount.id);  //add account ID for each record deleted
      }

       List<Contact> deletedContacts=[select id, AccountId,  Name from contact where AccountId IN: theIDs];
       for (Contact theContact: deletedContacts)
       {
        deletedRecord = new EntityHistory__c(); 
        deleted.Name = 'Contact: ' + theContact.Name;
        deletedRecord.Deleted_Contact_ID__c = theContact.id;
        deletedRecord.Deleted_Account_ID__c = theContact.AccountId;
        deletedRecord.Type__c = 'Cascade';
        listDeletedRecords.add(deletedRecord);
       }
       //Insert all the records into the Entity History file that were processes with this run  
       if (listDeletedRecords.isEmpty() == false){
      try
        {
            insert listDeletedRecords;
        }
     catch(Exception ex)
     {   
        System.debug('\n\nException ='+ex.getMessage()+'\n\n');
     }
  
}//End If
      
}