Pete's mistake in his conclusion is that he stated the quadrilaterals were congruent when he used a sequence of transformations that included a dilation. Dilation changes the size of the figure while maintaining shape, thus the shapes are similar but not congruent.
In his conclusion, Pete made an error by stating that the quadrilaterals A, B, C, D, and E, F, G, H are congruent because he used a sequence of rigid transformations. However, transformations that include a dilation are not rigid transformations. Rigid transformations, such as rotations, reflections, or translations, preserve the shape and size of the figure, making the resulting figure congruent to the original. A dilation, however, changes the size of the figure while maintaining its shape, resulting in a figure similar to, but not congruent with, the original. Therefore, although Pete was able to map quadrilateral A, B, C, D onto E, F, G, H, the two shapes are not congruent because dilation was a part of the sequence of transformations he used.
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Answer:
Pete didn't use only rigid transformations, so the figures are not congruent
Step-by-step explanation:
Translations, reflections, and rotations are all rigid transformations while a dilation is not. Pete used a dilation to make the shape smaller after transforming it, therefore the shape is similar not congruent.
If you're confused with what these math terms mean:
A rigid transformation (also called an isometry) is a transformation of the plane that preserves length.
In geometry, a reflection is a type of rigid transformation in which the preimage is flipped across a line of reflection to create the image. Each point of the image is the same distance from the line as the preimage is, just on the opposite side of the line.
A dilation is a type of transformation (not a rigid one though) that changes the size of the image. The scale factor, sometimes called the scalar factor, measures how much larger or smaller the image is.
Transformation involves moving an object from its original position to a new position.
Rotation is a transformation that turns a figure about a fixed point called the center of rotation. An object and its rotation are the same shape and size, but the figures m
