Given a set S of n points, we show that the length of 1) the minimum weight triangulation (MWT ) of the minimum weight convex partition (MWCP ) of S (TMWCP ) is at most Θ(n) longer than the MWT of S if collinearity of two or more edges is allowed and Θ(log n) otherwise, 2) the MWT of the minimum spanning tree (MST ) of the MWCP of S (Tmst(MWCP )) is at most Θ(n) longer than the MWT of S if coll...