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 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¯¯¯¯¯¯¯¯.

Question

GPT-4o mini · Answer

To prove that quadrilateral ABCD is a parallelogram, one of the key properties is that the opposite sides must be equal in length. If we consider the segments EB and ED as part of the diagonals in the context of triangle congruence or quadrilateral properties, the correct option related to EB and ED for ABCD to be a parallelogram would be:

EB must be the same length as ED.

This equality indicates that the segments are equal, which supports the properties of parallelograms where opposite sides (or diagonals of the congruent triangles formed) are equal in length.