Answer:Carly's statement, "All pairs of rectangles are dilations," is incorrect because not all pairs of rectangles are dilations of each other.
A pair of rectangles that would prove Carly's statement wrong is a pair that are not similar shapes. For two shapes to be dilations of each other, they must be similar shapes that differ only by a uniform scale factor.
Therefore, a counterexample pair of rectangles that would prove Carly's statement incorrect is a pair that have:
Different side lengths
Different width-to-length ratios
For example:
Rectangle A with dimensions 4 cm by 6 cm
Rectangle B with dimensions 8 cm by 12 cm
Since the side lengths and width-to-length ratios of these two rectangles are different, they are not similar shapes. And since they are not similar shapes, they do not meet the definition of a dilation.
So in summary, any pair of rectangles that:
Have different side lengths
Have different width-to-length ratios
Would prove that not all pairs of rectangles are dilations, and thus prove Carly's statement incorrect. The key to disproving Carly's statement is finding a pair of rectangles that are not similar shapes.
Hope this explanation helps! Let me know if you have any other questions.
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