To prove that a quadrilateral STUV is a parallelogram, one of the established criteria is that either pair of opposite sides must be congruent or parallel. Looking at the options provided, we can evaluate the conditions:
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ST is congruent UV and TU is congruent SV: This statement indicates that both pairs of opposite sides are congruent, which is a sufficient condition for STUV to be a parallelogram.
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SO is congruent TO and UO is congruent VO: This statement concerns segments from the center O to the vertices, which does not directly prove STUV is a parallelogram in terms of the properties regarding the sides.
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ST is congruent TU and UV is congruent SV: This statement shows that one pair of opposite sides (ST and UV) is congruent, but it does not indicate that the other pair (TU and SV) is opposing congruently.
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SO is congruent VO and TO is congruent UO: This statement also deals with segments from the center O, which does not provide the necessary evidence about the sides being congruent.
Given these options, the first option, ST is congruent UV and TU is congruent SV, is the correct choice. This establishes that STUV has two pairs of opposite sides that are congruent, which satisfies one of the properties needed to prove that STUV is a parallelogram.
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