Remember the transformations you have learned and their properties. Are all of them isometries?
See solution.
Practice makes perfect
Let's begin by remembering the fours types of transformations we've learned.
We have that the translations, reflections, and rotations are isometries, so they preserve angle measures and distances. Then, by applying them we can create congruent figures.
Dilations preserve angle measures, and the sides of the preimage and the image are proportional. Then we can apply them to produce similar figures.
To produce equal figures, we can consider three cases:
A dilation with scale factor 1 keeps the preimage and the image exactly the same.
If a figure has line symmetry, we can apply a reflection across its line of reflection and obtain the same figure.
If a figure has rotational symmetry, we can rotate it about its center of rotation and obtain the same figure.
