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}congoverline{vo}) and (overline{to}congoverline{uo})
○ (overline{so}congoverline{to}) and (overline{uo}congoverline{vo})
○ (overline{st}congoverline{tu}) and (overline{uv}congoverline{sv})
○ (overline{st}congoverline{uv}) and (overline{tu}congoverline{sv})

Explanation:

Step1: Recall parallelogram property

In a parallelogram, the diagonals bisect each other. If \(O\) is the center (inter - section point of the diagonals) of parallelogram \(STUV\), the diagonals \(SV\) and \(TU\) are bisected at \(O\). That means the segments formed by the bisection are congruent. So, \(\overline{SO}\cong\overline{VO}\) and \(\overline{TO}\cong\overline{UO}\).

Answer:

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