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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 STUV is a parallelogram, you need to establish that either opposite sides are congruent or that the diagonals bisect each other. Among the provided options, the one that directly states the necessary conditions for a parallelogram regarding opposite sides is:

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

This means that side ST is congruent to side UV and side TU is congruent to side SV, which confirms that STUV is a parallelogram by the property that the opposite sides are equal in length.

So, the correct choice is:

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