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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

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

1 answer

To prove that a quadrilateral STUV is a parallelogram, it is essential to show that either the opposite sides are equal and/or parallel. One of the common ways to establish this is by showing that the diagonals bisect each other, or that opposite sides are equal in length.

In this case, it seems the options provided are based on the segments connecting the points. The best choice according to standard geometric properties would be the statement that shows congruence of opposite sides, which is a sufficient condition to prove a parallelogram.

Looking at the responses:

  1. ST ≅ TU and UV ≅ SV: This claims that opposite sides are congruent, but it incorrectly lists adjacent sides instead of opposite sides.

  2. SO ≅ TO and UO ≅ VO: This discusses the segments from center O to the vertices but does not address the sides of the parallelogram.

  3. ST ≅ UV and TU ≅ SV: This correctly states that opposite sides are congruent, which is a correct way to demonstrate that STUV is a parallelogram.

  4. SO ≅ VO and TO ≅ UO: Similar to the earlier option discussing segments from the center to the vertices, this doesn’t provide relevant information about the sides needed for proving the shape is a parallelogram.

Therefore, the best option to show STUV is a parallelogram is: ST ≅ UV and TU ≅ SV.