The Exploring rigid transformations and congruence exercise appears under the 8th grade (U.S.) Math Mission and the High school geometry Math Mission. This exercise practices using a composition of various isometries to map one polygon into another.
Types of Problems
There is one type of problem in this exercise:
- Transform polygon into the other and answer question: This problem provides a grid with two polygons that should appear to be congruent. The user is asked to define a sequence of rigid maps that can transform one polygon into the other. After completed, the student is asked to determine if the polygons are congruent or not.
- A translation is a slide, a rotation is a turn and a reflection is a flip.
- It is recommended first to reflect (over any line) if orientation is reversed.
- Once orientation is correct, it is recommended to move any vertex onto a corresponding vertex via a translation.
- One a vertex is aligned, a rotation about that vertex will move the polygon as close as it possibly can get to the other polygon.
- Two shapes are congruent if and only if they can be lined up perfectly.
- If the shapes are not similar, it is not necessary to perform any transformations, one may just click "not similar" and submit.
- Pattern recognition is useful for developing Frieze patterns as well as on certain intelligence tests (such as IQ tests).
- An ability to visualize how shapes move can assist with many activities from completing jigsaw puzzles to packing boxes more efficiently.