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Question

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.

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¯¯¯¯¯¯¯¯.

EB ¯¯¯¯¯¯¯¯¯ must be half of the length of ED¯¯¯¯¯¯¯¯.
EB ¯¯¯¯¯¯¯¯¯ must be half of the length of ED¯¯¯¯¯¯¯¯.

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

Answer 1

To prove that quadrilateral ABCD is a parallelogram using the diagonals, we need to establish a relationship between the segments EB and ED. In a parallelogram, the diagonals bisect each other, which means that the segments connecting the intersection point (E) to the vertices (B and D) should be equal in length.

Therefore, the correct statement is:

EB must be the same length as ED.

This indicates that the segments EB and ED are equal in length, confirming that the diagonals bisect each other, which is a property of parallelograms.

So the correct response is: EB ¯¯¯¯¯¯¯¯¯ must be the same length as ED¯¯¯¯¯¯¯¯.