The null result of the Michelson-Morley experiment and the constancy of the one-way speed of light in the "rest system" are used to formulate a simple problem, to be solved by elementary geometry techniques using a pair of compasses and non-graduated rulers. The solution consists of a drawing allowing a direct visualization of all the fundamental effects of standard relativistic kinematics, namely time dilation, length contraction and relativity of simultaneity. Moreover, it also provides an immediate image of other important and more subtle aspects, often passed by in relativity courses, such as the conventionality of simultaneity thesis, possible non-invariance of the one-way speed of light and compatibility between the Lorentz-Poincare and Einstein-Minkowski philosophies. The geometric scheme so constructed constitutes a powerful tool to clearly illustrate both traditional and not-so-traditional aspects of special relativity teaching. (Contains 5 figures.)