Question

in quadrilateral abdc, (overline{ab}paralleloverline{cd}). which additional piece of information is needed to determine that abdc is a parallelogram?
o (overline{ab}congoverline{cd})
o (overline{ac}congoverline{bd})
o (overline{ab}perpoverline{bd})
o (overline{cd}perpoverline{bd})

Explanation:

Step1: Recall parallelogram properties

One of the definitions of a parallelogram is a quadrilateral with one - pair of opposite sides parallel and congruent. Given \(AB\parallel CD\), if \(AB\cong CD\), then \(ABDC\) is a parallelogram.

Step2: Analyze other options

• If \(AC\cong BD\), the quadrilateral could be an isosceles trapezoid.
• If \(AB\perp BD\) or \(CD\perp BD\), the quadrilateral is not necessarily a parallelogram.

Answer:

\(AB\cong CD\) (corresponding to the first option in the multiple - choice list)