Precisely defining rigid transformations

The  exercise appears under the Geometry Math Mission. This exercise practices using knowledge about the precise descriptions of the rigid transformations and their properties in various situations.

Types of problems
There is are three types of problems in this exercise:
 * 1) Decide whether each sequence of transformations always preserves the length of all segments and the measure of all angles.: This problem contains a table and user is asked to decide if each sequence of transformations always preserves the length of all segments and the measure of all angles by clicking the circles on the table.
 * 2) Which types of transformations could __ be?: This problem provides a graph with a brief explanation of how points maps to each other in a transformation. User is asked to find it the transformation is a rotation, a translation, or none of the above. There could be more than one answer for this type of problem.
 * 3) Which of the following transformations could map triangle ___ to ___ ?: This problem has a graph of a triangle and its image ___ shown below. User is asked to find which of the following transformations could map it. There may be more than one answer to this type of problem.

Strategies
Basic knowledge of reflections, transformations, and dilations are required for this exercise.
 * 1) Reflections are rigid transformations and preserve both angle measures and segment lengths.
 * 2) Dilations preserve angle measures, but not segment lengths.
 * 3) Therefore, performing a dilation after a reflection will change segment lengths but preserve all angle measures.
 * 4) Translations are also rigid transformations and preserve both angle measures and segment lengths.
 * 5) Dilations preserve angle measures, but not segment lengths.
 * 6) Therefore, performing a dilation after a translation will change segment lengths but preserve all angle measures.