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

Question

Possible Answers:
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 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 ST¯¯¯¯¯¯¯≅TU¯¯¯¯¯¯¯ and UV¯¯¯¯¯¯¯¯ ≅SV¯¯¯¯¯¯¯

Answer 1

To prove that quadrilateral STUV is a parallelogram, one of the following conditions must hold true:

1. Both pairs of opposite sides are congruent: This means that \( \overline{ST} \cong \overline{UV} \) and \( \overline{TU} \cong \overline{SV} \).
2. One pair of opposite sides is both congruent and parallel.
3. The diagonals bisect each other.

Considering the options you provided, the following option states a correct condition for proving that STUV is a parallelogram:

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

• This means that the opposite sides \( ST \) and \( UV \) are congruent, as well as \( TU \) and \( SV \).

Therefore, the answer that must be true to prove that STUV is a parallelogram is: ST¯¯¯¯¯¯¯≅UV¯¯¯¯¯¯¯¯ and TU¯¯¯¯¯¯¯ ≅SV¯¯¯¯¯¯¯.