Defining similarity through angle-preserving transformations

The  exercise appears under the Geometry Math Mission. This exercise uses a manipulative to explore geometric transformations and better understand how they are connected with the similarity relation.

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


 * 1) Find a composition of maps: This problem provides two shapes that may possibly be similar. The student is asked to determine if they are similar by trying to construct a sequence of transformations that will map one onto the other.Dstapt1.png
 * 2) Determine which statements are correct: This problem provides a diagram and some information. The student is asked to determine which, if either, or a collection of statements are necessarily true.Dstapt2.png

Strategies
Knowledge of similitudes and familiarity with the Cartesian coordinate plane are encouraged to ensure success on this exercise.
 * 1) On the Find a composition of maps problem, one way to effective find a correct sequence of transformations is to translate a point in one polygon to a corresponding point on the other one. Once this is completed reflecting, rotating and dilating as needed may be more obvious.
 * 2) The rotations appear to always be multiples of forty-five degrees.
 * 3) On the Perform the transformations on the polygon problem, the transformations of rotation, reflection, dilation  and translation are all similitudes. Therefore using these preserves similarity.

Real-life Applications

 * 1) Triangle similarity is the foundation of trigonometry and it's multitude of applications in the sciences.