A transformation that maps a preimage onto an image such that the preimage and image are congruent is called an isometry. There are exactly four types of isometries in the plane.
I. Composition of Reflections Across Parallel Lines.
1. Reflect the polygon ABCD across line e.
2. Reflect A'B'C'D' across line f and hide the image A'B'C'D'.
3. Compare ABCD to A"B"C"D". What type of single transformation maps ABCD onto A"B"C"D"?
4. Find the single transformation that maps ABCD onto A"B"C"D". Be specific (distance and direction).
5. A composition of reflections across two parallel lines is a _______________.
II. Composition of Reflections Across Intersecting Lines
1. Reflect the polygon ABCD across line e.
2. Reflect A'B'C'D' across line f and hide the image A'B'C'D'.
3. Compare ABCD to A"B"C"D". What type of single transformation maps ABCD onto A"B"C"D"?
4. Find the single transformation that maps ABCD onto A"B"C"D". Be specific (angle and center).
5. A composition of reflections across two intersecting lines is a _______________.
III. Glide Reflections
1. Translate the polygon ABCD along the vector FE.
2. Reflect A'B'C'D' across line f and hide the image A'B'C'D'.
3. Compare ABCD to A"B"C"D". This type of transformation that maps ABCD onto A"B"C"D" is called a glide reflection.
*In a plane, one of two congruent figures can be mapped onto the other by a composition of at most __________ reflections.