This study focuses on the geometric properties of rotating triangles, aiming to analyze the effects of rotational operations on the internal structure of a triangle. We investigate the geometric characteristics of new triangles formed when an arbitrary point in the plane is rotated by a specific angle around the vertices of a given triangle. Using coordinate geometry, we examine the transformations of coordinates, area relationships, and the similarity and angular properties that emerge under particular ratios of rotation angles. Furthermore, the study explores the equations of lines and circles under specific conditions in which the area of the rotated equilateral triangle becomes zero. The results reveal the relationships between the ratios of rotation angles and the geometric properties of the resulting triangles, and suggest potential directions for future research, such as extending the analysis to other angle ratios and studying the combined effects of rotation and translation on area variation.