Geometry is required for many secondary school students, and is often learned, taught, and assessed more in a heuristic image-based manner, than as a formal axiomatic deductive system. Students are required to prove general theorems, but diagrams are usually used. It follows that understanding how students engage in perceiving and reasoning about such diagrams can provide educators with greater insights into learning, instruction, and assessment of these matters. Simply put, the end in view of this research program should provide as much insight as possible into two fundamental questions for any given learner considering a geometrical diagram. Firstly, what aspects of that diagram are being perceived from one moment to the next, and, secondly, in what manners are those aspects of the diagram being considered. It assumed here that such a learner is having their brain waves monitored by an electroencephalograph and that the geometrical diagram is being presented on an eye-tracking monitor, recording their point of gaze. Accordingly, in this study we seek to identify brain and body activities that correlate in valid and reliable manners, and with a high degree of statistical significance, with different aspects of geometrical image-based perception and reasoning. In so doing, we seek a better understanding of cognitive processes associated with geometrical image-based learning, instruction, and assessment in mathematics education, and to contribute to extending multidisciplinary boundaries of educational research. (Contains 8 figures and 1 table.)