Question

if you were to prove that quadrilateral abcd is a parallelogram, what would need to be true about eb and ed? (1 point)

○ eb must be the same length as ed.
○ eb must be half of the length of ed.
○ ed must be a different length than eb.
○ ed must be half of the length of eb.

Explanation:

Step1: Recall the property of a parallelogram's diagonals

In a parallelogram, the diagonals bisect each other. That is, if \(ABCD\) is a parallelogram with diagonals \(AC\) and \(BD\) intersecting at point \(E\), then \(AE = EC\) and \(BE=ED\).

Step2: Analyze the given options

• If \(\overline{EB}\) must be the same length as \(\overline{ED}\), this satisfies the property that the diagonals of a parallelogram bisect each other.
• If \(\overline{EB}\) must be half of the length of \(\overline{ED}\), it does not satisfy the diagonal - bisecting property of a parallelogram.
• If \(\overline{ED}\) must be a different length than \(\overline{EB}\), it contradicts the diagonal - bisecting property of a parallelogram.
• If \(\overline{ED}\) must be half of the length of \(\overline{EB}\), it also contradicts the diagonal - bisecting property of a parallelogram.

So, for quadrilateral \(ABCD\) to be a parallelogram, \(\overline{EB}\) must be the same length as \(\overline{ED}\).

Answer:

$\overline{EB}$ must be the same length as $\overline{ED}$.