This study compares American and Korean curriculum standards, textbooks, and geometry items to help explain the consistent differences that have been found between the achievement levels of U.S. and Korean students in the Program for International Student Assessment (PISA) mathematics. Since PISA measures the mathematical proficiency of 15-year-old students, this study focuses primarily on 8th-grade curriculum standards and textbooks. The findings provide valuable information for curriculum designers and textbook editors to help improve the quality of geometry curricula and textbooks. Teachers can also use these findings to assess the proficiency levels of items in the textbooks they use, so that they can develop lesson plans appropriate to the ability of their students and select relevant problems for their classes.