Parallel & Skew Synthesis Problem (I)
- Tim Brzezinski
- Straight Lines
Directions: Shown below is a picture of a rectangular prism. Your job is to label its 8 vertices ("corner points") with the purple CAPITAL LETTERS off to the right so that ALL the criteria listed below are TRUE. (Simply drag a letter next to any vertex of the prism.) Note: If you wish to change the appearance of the prism, simply move (drag) any one (or more) of the 3 blue vertices around. Again, label each of the prism's 8 vertices with the letters off to the right so that ALL the following statements are TRUE: 1) The line passing through M & K is parallel to the line passing through P & J. 2) The line passing through J & W is parallel to the line passing through K & S. 3) Points S, R, W, & T are coplanar. 4) Points T, P, R, & M are coplanar. 5) The line passing through J & W is skew with the line passing through M & P, the line passing through S & T, and the line passing through S & R. 6) No combination of any 3 vertices (out of the 8 the prism has) are collinear. 7) Points P, K, R, & S are coplanar. 8) The line passing through M & T is parallel to the line passing through P & R.
One question: Which condition, in #(1) - (8) above, would ALWAYS be met, regardless of how you label the vertices?