Converse Parallelogram Proofs Quick Check

Question

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Question
Edwidge draws parallelogram STUV with a center at O. What must be true to prove that STUV is a parallelogram?(1 point)
Responses

SO¯¯¯¯¯¯¯≅TO¯¯¯¯¯¯¯ and UO¯¯¯¯¯¯¯¯ ≅VO¯¯¯¯¯¯¯¯
line segment cap s cap o is congruent to line segment cap t cap o A n d line segment cap u cap o comma line segment cap t cap o and line segment cap u cap o is congruent to line segment cap v cap o

SO¯¯¯¯¯¯¯≅VO¯¯¯¯¯¯¯¯ and TO¯¯¯¯¯¯¯ ≅UO¯¯¯¯¯¯¯¯
line segment cap s cap o is congruent to line segment cap v cap o and line segment cap t cap o comma line segment cap v cap o A n d line segment cap t cap o is congruent to line segment cap u cap o

ST¯¯¯¯¯¯¯≅UV¯¯¯¯¯¯¯¯ and TU¯¯¯¯¯¯¯ ≅SV¯¯¯¯¯¯¯
line segment cap s cap t is congruent to line segment cap u cap v A n d line segment cap t cap u comma line segment cap u cap v and line segment cap t cap u is congruent to line segment cap s cap v

ST¯¯¯¯¯¯¯≅TU¯¯¯¯¯¯¯ and UV¯¯¯¯¯¯¯¯ ≅SV¯¯¯¯¯¯¯

Answer 1

To prove that quadrilateral STUV is a parallelogram, it is sufficient to show that either one pair of opposite sides are congruent or that the diagonals bisect each other.

In this case, since the question mentions the center O and looks at line segments involving O, the most relevant choice is the one that references the congruence of segments from the center to the vertices.

Given the options you provided, the correct response that directly leads to establishing STUV as a parallelogram is:

SO¯¯¯¯¯¯¯≅TO¯¯¯¯¯¯¯ and UO¯¯¯¯¯¯¯¯ ≅VO¯¯¯¯¯¯¯¯

This asserts that the segments connecting the center O to the vertices S and T are congruent, and similarly for U and V, which is valid for establishing properties related to the symmetry and equal lengths in a parallelogram configuration.

If there's an error or specific instruction leading to a different answer, please clarify!