Question

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

In a parallelogram, the diagonals bisect each other. That is, if \(O\) is the center (intersection point of diagonals \(SV\) and \(TU\)), then \(SO = VO\) and \(TO=UO\)

Answer:

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