Question

Question

Use the image to answer the question.

A parallelogram has vertices upper A, upper B, upper C, and upper D. Opposite vertices are connected via diagonal lines that intersect at an interior point labeled upper E. Sides upper A upper D and upper B upper C are much longer than the other sides.

If you were to prove that quadrilateral ABCD is a parallelogram, what would need to be true about EB and ED?

(1 point)
Responses which answer is correct and why

EB ¯¯¯¯¯¯¯¯¯ must be the same length as ED¯¯¯¯¯¯¯¯.
EB ¯¯¯¯¯¯¯¯¯ must be the same length as ED¯¯¯¯¯¯¯¯.

ED ¯¯¯¯¯¯¯¯¯ must be half of the length of EB¯¯¯¯¯¯¯¯.
ED ¯¯¯¯¯¯¯¯¯ must be half of the length of EB¯¯¯¯¯¯¯¯.

ED ¯¯¯¯¯¯¯¯¯ must be a different length than EB.¯¯¯¯¯¯¯¯¯
ED ¯¯¯¯¯¯¯¯¯ must be a different length than EB.¯¯¯¯¯¯¯¯¯

EB ¯¯¯¯¯¯¯¯¯ must be half of the length of ED¯¯¯¯¯¯¯¯.
EB ¯¯¯¯¯¯¯¯¯ must be half of the length of ED¯¯¯¯¯¯¯¯.
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Answer 1

To prove that quadrilateral ABCD is a parallelogram, you need to show that the diagonals bisect each other. In the context of the given problem, that means the segments EB and ED must be equal in length.

Therefore, the correct answer is:

EB must be the same length as ED.

In a parallelogram, the diagonals bisect each other at their intersection point. This means that if E is the point of intersection of the diagonals AC and BD, then:

EB = ED.

This relationship is a key property of parallelograms and is necessary to establish that ABCD is indeed a parallelogram based on the given information about the vertices and intersections.