Two answers needed.  The Poncelet-Steiner theorem states that one is unnecessary if you can use the other one, and the Mohr-Mascheroni theorem says one of them is unnecessary. One can be used, along with dividers, to create the Pythagorean extensions of the rationals. Considered in algebraic terms, they can only produce constructible numbers, and as a result one cannot construct every regular polygon with them, nor can one double the volume of a 
Two answers needed.  The Poncelet-Steiner theorem states that one is unnecessary if you can use the other one, and the Mohr-Mascheroni theorem says one of them is unnecessary. One can be used, along with dividers, to create the Pythagorean extensions of the rationals. Considered in algebraic terms, they can only produce constructible numbers, and as a result one cannot construct every regular polygon with them, nor can one double the volume of a cube with them.  One also cannot use them to find a square with the area of a given circle, but with a quadratrix, one can trisect a curve with them. For 10 points, identify these two mechanical devices used in classical Greek geometry.
Two answers needed.  The Poncelet-Steiner theorem states that one is unnecessary if you can use the other one, and the Mohr-Mascheroni theorem says one of them is unnecessary.
straightedge and compass [prompt on "ruler" for straightedge; accept answers in either order]