Composing moves, symmetry and the reflection trick
Meet two reflections in a row, the glide reflection, the axes of symmetry of a polygon and the shortest path found with a reflection.
- Germany: grade 10
- Iran: grade 11
- Syria: grade 11
- Ukraine: grade 9
- Russia: grade 9
Guide
This studio is for Iran's Grade 11 geometry 2 (chapter 2, transformations and their uses).
A move that keeps the length of every segment is an isometry. Reflections, translations and rotations are isometries. A point the move does not shift is a fixed point; every point of the mirror line is fixed.
Doing two moves one after the other gives a new move. Two reflections in parallel lines make a translation. A reflection followed by a slide along the mirror is a glide reflection.
Moves also solve problems: for the shortest path we reflect one of the points so that the bent path becomes a straight line.