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Carly stated, “All pairs of rectangles are dilations.” Which pair of rectangles would prove that Carly’s statement is incorrect?

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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.

Explanation:

User RobJohnson
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