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.

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

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

Answer 1

To prove that quadrilateral ABCD is a parallelogram using the diagonals AE and CE that intersect at point E, it is necessary to show that segments EB and ED are equal in length. This is due to the property of parallelograms where the diagonals bisect each other.

Therefore, the correct response is:

EB must be the same length as ED.