### Automatic Synthesis of Geometry Problems for an Intelligent Tutoring System

### Abstract

This paper presents a semi-automated methodology for generating
geometric proof problems of the kind found in a high-school
curriculum. We formalize the notion of a geometry proof problem and
describe an algorithm for generating such problems over a
user-provided figure. Our experimental results indicate that our
problem generation algorithm can effectively generate proof
problems in elementary geometry.
On a corpus of 110 figures taken from popular geometry textbooks,
our system generated an average of about 443 problems per figure
in an average time of 4.7 seconds per figure.