To categorize the descriptions based on whether the side lengths would allow for many different polygons or would make one unique polygon, we can analyze the lengths given.
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Would allow you to make many different polygons - These sets of side lengths can form a variety of polygons because they can have various combinations and configurations. No set of side lengths is forming a triangle or polygon with strict constraints leading to a unique polygon shape.
- Side lengths of 4, 6, 7, and 9: This set can create multiple different polygons.
- Side lengths of 6, 8, 9, and 11: This set can also create multiple different polygons.
- Side lengths of 9, 11, 12, and 14: This set can create multiple different polygons.
- Side lengths of 9.3, 8.5, 14.5: This set can create multiple different polygons.
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Would make one unique polygon - These sets have specific lengths where only one polygon (often a triangle) can be formed because they meet the conditions for a specific shape.
- Side lengths of 7, 1, 8, 3, 7, 5, and 2, 1: With these lengths, you could only uniquely construct a polygon based on their values.
Thus, the sorted categories would be:
Would allow you to make many different polygons:
- Side lengths of 4, 6, 7, and 9
- Side lengths of 6, 8, 9, and 11
- Side lengths of 9, 11, 12, and 14
- Side lengths of 9.3, 8.5, 14.5
Would make one unique polygon:
- Side lengths of 7, 1, 8, 3, 7, 5, and 2, 1
(Note: If the side lengths specified for unique shapes indeed include multiple values but lead to scenarios where only one polygon fits, that would apply for those specified as needing detection rather than observed.)
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