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

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

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

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

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
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1 answer

To prove that quadrilateral STUV is a parallelogram, we can use the property that opposite sides of a parallelogram are congruent. The correct response that establishes this proves the necessary conditions for a quadrilateral to be recognized as a parallelogram.

The correct answer is:

ST ≅ UV and TU ≅ SV

This is shown by the response:

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

Explanation:

  1. Definition of a Parallelogram: A quadrilateral is a parallelogram if either one of the following conditions is true:

    • Opposite sides are congruent.
    • Opposite angles are congruent.
    • The diagonals bisect each other.
    • One pair of opposite sides is both parallel and congruent.

  2. Reason for Correctness: In this case, proving that \( ST \cong UV \) indicates that one pair of opposite sides are congruent, and \( TU \cong SV \) indicates that the other pair of opposite sides are also congruent. This satisfies the definition of a parallelogram, affirming that STUV is indeed a parallelogram.

In contrast, the other options revolve around segments connecting the center O but do not directly support the primary conditions needed to establish the sides of the quadrilateral STUV as congruent necessary for it to be classified as a parallelogram. Thus the first choice is the clearest and most direct proof of STUV being a parallelogram.