Practice with the Four Isometries: Translation, Rotation, Reflection, and Glide

① This GeoGebra example provides an interactive practice for the four isometries (translation, rotation, reflection, and glide reflection) by transforming a given figure and observing the resulting images. ② The core mathematical concept is isometry, a transformation that preserves distances and shapes, including translation (using vectors), rotation (using an angle), reflection (using a line as mirror), and glide reflection (a combination of reflection and translation). ③ Construction details: from the summary, the commands used include Vector (to define translation direction), Translate (to perform translation), Rotate (with angle α for rotation), Line (to define mirror axis), Mirror (for reflection), and Point (to mark vertices). The objects include multiple transformed copies (e.g., pic1', pic1'_1, etc.) and text labels (text1–text8) for instructions. ④ This is suitable for middle school or high school geometry classes, useful for teachers demonstrating transformations or for students exploring properties such as distance preservation, angle preservation, and symmetry.