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 EB ¯¯¯¯¯¯¯¯¯ must be the same length as ED¯¯¯¯¯¯¯¯. EB ¯¯¯¯¯¯¯¯¯ must be the same length as ED¯¯¯¯¯¯¯¯. 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¯¯¯¯¯¯¯¯. ED ¯¯¯¯¯¯¯¯¯ must be a different length than EB.¯¯¯¯¯¯¯¯¯

Answer 1

In order to prove that quadrilateral ABCD is a parallelogram, one property that can be used is that the diagonals of a parallelogram bisect each other. If point E is the midpoint of diagonal AC, then for ABCD to be a parallelogram, the segments \( EB \) and \( ED \) must satisfy the condition that the lengths are equal, since points B and D would lie on different sides of the midpoint.

Therefore, the necessary condition would be:

EB must be the same length as ED.

This indicates that both segments are equal in length, supporting the property that diagonals bisect each other in a parallelogram.