Exploring angle-preserving transformations and similarity

The  exercise appears under the 8th Grade Math Mission. This exercise practices using a composition of various isometries and similitudes to map one polygon into another.

Types of Problems
There is one type of problem in this exercise:


 * 1) Transform polygon into the other and answer question: This problem provides a grid with two polygons that should appear to be similar. The student is asked to define a sequence of maps that can transform one polygon into the other. After completed, the student is asked to determine if the polygons are similar or not.Eaptans1.png

Strategies
The manipulative makes accuracy badges straightforward on this exercise. Efficiency will come from with experience and practice with earlier transformation exercises.
 * 1) A translation is a slide, a rotation is a turn and a reflection is a flip. These maps preserve angle measure and lengths.
 * 2) It is recommended first to reflect (over any line) if orientation is reversed.
 * 3) Once orientation is correct, it is recommended to move any vertex onto a corresponding vertex via a translation.
 * 4) One a vertex is aligned, a rotation should be done to align sides about that vertex.
 * 5) Finally, a dilation should be used to shrink or enlarge the shape to the correct size.
 * 6) Two shapes are similar if and only if they can be lined up perfectly.
 * 7) If the shapes are not similar, it is not necessary to perform any transformations, one may just click "not similar" and submit.

Real-life applications

 * 1) Pattern recognition is useful for developing Frieze patterns as well as on certain intelligence tests (such as IQ tests).
 * 2) An ability to visualize how shapes move can assist with many activities from completing jigsaw puzzles to packing boxes.
 * 3) This spatial reasoning including dilations can be used in many types of visual arts.