To determine whether the two shapes are congruent, similar, both, or neither, we need to analyze the given dimensions: 9 inches, 6 inches, 3 inches, and 2 inches.
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Congruent Figures: Two figures are congruent if they have the exact same shape and size. This means that all corresponding sides are equal in length.
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Similar Figures: Two figures are similar if they have the same shape (corresponding angles are equal) and their corresponding sides are in proportion (the ratios of corresponding side lengths are equal).
Let's look at the ratios of the sides:
- If we take one shape with sides 9 inches, 6 inches, and 3 inches, we can explore the proportions with the other shape that has sides 2 inches and the others that would maintain similarity with those sides.
If we assume a second shape has sides proportional to the ones we have:
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The ratio between 9 and the corresponding side in the other shape (let's denote that as x):
- \( \frac{9}{x} \)
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The ratio between 6 and the corresponding side in the other shape (let's denote that as y):
- \( \frac{6}{y} \)
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The ratio between 3 and the corresponding side in the second shape (let's denote that as z):
- \( \frac{3}{z} \)
For similar figures, these ratios must be equal.
However, without any identified specifics for the second shape, we can't definitively say if they're congruent or similar. However, if we suppose that the second shape consists of a proportional scale with sides such as 2 inches to some factor:
- Using the data given, we do not have equal corresponding angles or sides to directly compare as similar or congruent.
Based on the dimensions provided, they cannot be congruent, and since no clear division in proportions can be made to establish similarity based just on numbers without specific angle relationships, they do not have clear similarity either.
Thus, the answer is:
C. Neither
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