Question

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

Answer 1

To prove that quadrilateral ABCD is a parallelogram, one important property we can examine is the relationship between the lengths of the diagonals in terms of their midpoints. If points E and D are the midpoints of segments AB and CD respectively, for ABCD to be a parallelogram, it is essential that the diagonals bisect each other.

In the context of comparing EB and ED:

The correct response would be that "EB must be the same length as ED." This statement indicates that the segments connecting the midpoints of opposite sides must be equal, which is a condition that supports the claim that ABCD is a parallelogram.

Therefore:

EB must be the same length as ED.