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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 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¯¯¯¯¯¯¯≅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¯¯¯¯¯¯¯≅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¯¯¯¯¯¯¯

1 answer

To prove that quadrilateral STUV is a parallelogram, you can use one of several properties related to the sides or the diagonals of the quadrilateral. The properties you provided include different conditions involving the congruence of segments.

The most relevant property to this situation is the one that states that if both pairs of opposite sides are congruent, the quadrilateral is a parallelogram. Thus, we need to show that:

  1. \( ST \cong UV \) (one pair of opposite sides)
  2. \( TU \cong SV \) (the other pair of opposite sides)

Among the options you provided, the one that fulfills this criterion is:

ST ≅ UV and TU ≅ SV

This confirms that both pairs of opposite sides are congruent, thus proving that STUV is a parallelogram.