Qualitatively defining rigid transformations

The  exercise appears under the Geometry Math Mission. This exercise explores the many qualitative aspects that are true about transformations and some that are not.

Types of Problems
There are three types of problems in this exercise:


 * 1) Decide which characterizations describe a transformation: This problem has a selection chart with descriptions on the left and categories along the top. The student is asked to determine if the description is certainly, might be, or is definitely not a specific transformation.Qualdrt1.png
 * 2) Which maps preserve what properties: This problem has a selection chart with several compositions of maps along the left and possible measures that could be preserved along the top. The student is asked to select which maps preserve which qualities.Qualdrt2.png
 * 3) Determine which kinds of transformations can do what is expected: This problem has a coordinate grid with some points labeled and a description detailing which points are sent to other points. The student is asked to determine, based on the assignment, which transformations could be specified.Qualdrt3.png

Strategies
Intimate knowledge of transformations is and a very discerning geometric eye are encouraged to ensure success on this exercise.
 * 1) Dilations preserve angle measure. Translations, reflections and rotations preserve both angles measure and length. One dimensional stretching preserves neither.
 * 2) A translation:
 * 3) will make a parallelogram
 * 4) will preserve parallel lines
 * 5) will move all points in the same direction
 * 6) A rotation:
 * 7) will make congruent angles and will have reference to angle measure, but must also preserve length
 * 8) A reflection:
 * 9) will have the reflection line as a perpendicular bisector of segments formed from preimage to image.

Real-life Applications

 * 1) A firm understanding of transformations is necessary for understanding some of the more intricate concepts in non-Euclidean geometry (a possible model of the universe).
 * 2) Transformations have applications in art and architecture.