Conjecture: As long as each of the two smaller pentagons are formed by joining the midpoints of the next larger pentagon, the two ratios of the areas will always be equal and the two ratios of the perimeters will always be equal, no matter what shape the largest pentagon has.

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Conjecture: As long as each of the two smaller pentagons are formed by joining the midpoints of the next larger pentagon, the two ratios of the areas will always be equal and the two ratios of the perimeters will always be equal, no matter what shape the largest pentagon has.

Under what conditions is this true?

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