Think about which transformations do not affect the shape of a figure.
Two figures are similar if one can be mapped onto the other using a sequence of translations, reflections, rotations, and dilations.
Practice makes perfect
We are asked to explain how similar figures are related by a sequence of transformations. Similar figures have the same shape and congruent angles, but they can have different sizes. Let's recall what we know about transformations, focusing on how they affect the shape and size of the figure.
Translation
A translation slides a figure around without turning it. It does not affect the shape or size of the figure.
Reflection
A reflection creates a mirror image of a figure. It does not affect the shape or size of the figure.
Rotation
A rotation turns a figure around a fixed point. It does not affect the shape or size of the figure.
Dilation
A dilation moves each point of a figure along the ray through the point, starting from a fixed center. It does not affect the shape of the figure, but it does affect its size.
Translations, reflections, rotations, and dilations map figures onto similar figures. Two figures are similar if one can be mapped onto the other using a sequence of translations, reflections, rotations, and dilations.
