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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

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¯¯¯¯¯¯¯
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
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1 answer

To prove that STUV is a parallelogram using its center O, the correct response is:

SO¯¯¯¯¯¯¯≅VO¯¯¯¯¯¯¯¯ and TO¯¯¯¯¯¯¯ ≅UO¯¯¯¯¯¯¯¯.

Reasoning:

In a parallelogram, the diagonals bisect each other. If O is the center of the parallelogram, then it is the midpoint of both diagonals ST and UV, as well as TU and SV. For STUV to be considered a parallelogram, we must show that the segments connecting the center (O) to the vertices (S, T, U, V) are congruent in pairs:

  1. SO ≅ VO indicates that the segment from point S to center O is congruent to the segment from point V to center O. This means that points S and V are equidistant to O.

  2. TO ≅ UO shows that the segment from point T to center O is congruent to the segment from point U to center O, indicating that points T and U are also equidistant from O.

Since these pairs of segments are congruent, it confirms that the opposite sides of the parallelogram are equal in length, which is a necessary condition for a figure to be a parallelogram. Thus, this response is the only one that demonstrates the necessary properties for STUV to be classified as a parallelogram.