Update Trigger

I would like to pull the Street_Full_Name and AnnoName columns from my Street Table Where StreetID in the Segment Table = StreetId in the Street Table when there has been a insertion or Update on my Street.
AS well i will need it to fire or a separate Trigger to fire when there has been and insertion or Update on the Segment table
How best to handle something like ?
Segment Table Trigger(which is not working)

ALTER TRIGGER [dbo].[FName_AName_Num_Las<wbr ></wbr>tdate_Cont<wbr ></wbr>_Segment] ON [dbo].[Segment]
    AFTER INSERT, UPDATE
AS
    BEGIN
        SET NOCOUNT ON;

       UPDATE Segment
        SET     Street_Full_Name = st.Street_Full_Name,
                AnnoName = st.AnnoName
        FROM    dbo.Segment s
                INNER JOIN INSERTED i ON s.OID = i.OID
                INNER JOIN dbo.Street st ON s.Street_ID = st.Street_ID

    END