This study investigates geometry teachers' evaluations of problems that use visual arts contexts. We ask, "how do teachers' evaluations relate to the four arguments justifying the geometry course?" and "How do teachers draw on the APPRAISAL system to evaluate sample geometry problems from textbooks?" Nine high school teachers were convened in three focus groups. We analyzed the teachers' discussions using systemic functional linguistics and identified 676 evaluations. Ninety percent of the evaluations pertained to the system of appreciation, including teachers' reactions to the problems, their stances about the problems' compositions, and their opinions about the problems' values. The teachers valued problems where students could appreciate the relevance of math in real-world scenarios, engage in math explorations, and become intrigued.