Question

idge draws parallelogram stuv with a center at o. what must be true to prove that stuv is a parallelogram? (1 point)
st ≅ uv and tu ≅ sv
so ≅ vo and to ≅ uo
st ≅ tu and uv ≅ sv
so ≅ to and uo ≅ vo

Explanation:

Step1: Recall parallelogram properties

One of the properties of a parallelogram is that the diagonals bisect each other. If \(O\) is the center (the intersection point of the diagonals), then for \(STUV\) to be a parallelogram, \(SO = VO\) and \(TO=UO\) (diagonals bisect each other).

Step2: Analyze other options

• For the first option \(\overline{ST}\cong\overline{UV}\) and \(\overline{TU}\cong\overline{SV}\), these are the properties of a parallelogram (opposite sides are congruent), but the problem is about the center \(O\) (related to diagonals).
• For the third option \(\overline{ST}\cong\overline{TU}\) and \(\overline{UV}\cong\overline{SV}\), this would imply adjacent sides are congruent (a rhombus - a special case of parallelogram, but not the general condition for a parallelogram based on the center \(O\)).
• For the fourth option \(\overline{SO}\cong\overline{TO}\) and \(\overline{UO}\cong\overline{VO}\), this does not follow the diagonal - bisecting property of a parallelogram.

Answer:

\(\overline{SO}\cong\overline{VO}\) and \(\overline{TO}\cong\overline{UO}\) (the second option)