To prove that a quadrilateral is a parallelogram, we need to establish that either pairs of opposite sides are equal, or pairs of opposite angles are equal, or that the diagonals bisect each other.
Looking through the provided options:
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Option A states that \( SO \cong VO \) and \( TO \cong UO \). This describes a situation where the segments from the center O to the vertices are equal, but does not directly establish the properties of the sides of the parallelogram.
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Option B states that \( ST \cong UV \) and \( TU \cong SV \). This option states that both pairs of opposite sides are equal, which is a property that defines a parallelogram.
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Option C states that \( ST \cong TU \) and \( UV \cong SV \). This option describes adjacent sides rather than opposite sides, and does not establish the properties required to prove a parallelogram.
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Option D states that \( SO \cong TO \) and \( UO \cong VO \). Similar to option A, it describes segments from the center to the vertices but does not address the side relationships needed.
Thus, Option B is the correct choice, as it satisfies the necessary condition to prove that STUV is a parallelogram by stating that both pairs of opposite sides are equal.
Correct answer: B. ST ≅ UV and TU ≅ SV.
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