Based on Steiner's fascinating theorem for trapezium, seven geometrical constructions using straight-edge alone are described. These constructions provide an excellent base for teaching theorems and the properties of geometrical shapes, as well as challenging thought and inspiring deeper insight into the world of geometry. In particular, this article also mentions the orthic triangle and proves its special property, and shows some other interesting constructions, such as, for example, how to construct a circle's diameter using straightedge alone and having only a segment with its midpoint. In addition, it is enhanced by aspects of the historical background of geometric constructions, including reference to "impossible constructions." Application of the material presented in college or high school can enhance students' appreciation of the elegance, beauty, and fascination of mathematics. Through such "adventures," students will be encouraged to further pursue geometric problems and explore various methods of problem solving, especially those concerned with geometric constructions.