Automated generation of high school geometric questions involving implicit construction

Abstract

We describe a framework that combines a combinatorial approach and automated deduction to generate geometry problems which require implicit constructions for their solution. This is an extension of our framework developed for generating geometric questions without construction. Such a system would help teachers to quickly generate large numbers of questions involving implicit construction on a geometry topic. Students can explore, revise and master specific topics covered in classes and textbooks based on construction-based generated questions. This system may also help standardize tests such as GMAT and SAT. Our novel methodology uses (i) a combinatorial approach for generating geometric figures and objects for construction (ii) automated deduction to generate new questions and solutions. By combining these methods, we are able to generate questions involving finding or proving relationships between geometric objects based on a specification of the geometry objects, concepts, theorems and construction object to be covered by the questions. Experimental results show that a large number of questions can be generated in a short time.