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

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

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¯¯¯¯¯¯¯¯

Answer 1

SO ≅ VO and TO ≅ UO.

Reason: If the diagonals bisect each other (each vertex-to-center segment equals its opposite), then the diagonals share midpoints, so the quadrilateral is a parallelogram.