Question

converse parallelogram proofs quick check
edwidge draws parallelogram ( stuv ) with a center at ( o ). what must be true to prove that ( stuv ) is a parallelogram? (1 point)
( overline{so} cong overline{vo} ) and ( overline{to} cong overline{uo} )
( overline{st} cong overline{uv} ) and ( overline{tu} cong overline{sv} )
( overline{st} cong overline{tu} ) and ( overline{uv} cong overline{sv} )
( overline{so} cong overline{to} ) and ( overline{uo} cong overline{vo} )

Explanation:

Step1: Recall parallelogram property

One of the properties of a parallelogram is that the diagonals bisect each other.

Step2: Analyze the segments

If \(O\) is the center (where the diagonals intersect), for \(STUV\) to be a parallelogram, the segments of the diagonals must be congruent. That is, if the diagonals are \(SV\) and \(TU\), then \(SO = VO\) (so \(\overline{SO}\cong\overline{VO}\)) and \(TO=UO\) (so \(\overline{TO}\cong\overline{UO}\)) as per the diagonal - bisecting property of parallelograms.

Answer:

$\overline{SO}\cong\overline{VO}$ and $\overline{TO}\cong\overline{UO}$