If you were to prove that quadrilateral ABCD is a parallelogram, what would need to be true about EB and ED ? (1 point) Responses EB ¯¯¯¯¯¯¯¯¯ must be the same length as ED¯¯¯¯¯¯¯¯. EB ¯¯¯¯¯¯¯¯¯ must be the same length as ED¯¯¯¯¯¯¯¯. 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¯¯¯¯¯¯¯¯. ED ¯¯¯¯¯¯¯¯¯ must be half of the length of EB¯¯¯¯¯¯¯¯. ED ¯¯¯¯¯¯¯¯¯ must be half of the length of EB¯¯¯¯¯¯¯¯.

Question

GPT-4o mini · Answer

To prove that quadrilateral ABCD is a parallelogram, one of the properties you can check is that the diagonals bisect each other. If EB and ED are segments that connect points on the diagonals of the quadrilateral, for ABCD to be a parallelogram, it must be true that EB must be the same length as ED. This means:

EB must be the same length as ED.

This property indicates that the segments connecting the intersection point of the diagonals bisect each other, which is a characteristic of parallelograms. Thus, the first option is the correct response.