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Question
Use the image to answer the 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
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¯¯¯¯¯¯¯¯.
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¯¯¯¯¯¯¯¯.
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page 16 of 17
1 answer
To prove that quadrilateral ABCD is a parallelogram using the properties of its diagonals, we can use the fact that the diagonals of a parallelogram bisect each other.
In the given scenario, point E is the intersection of the diagonals AC and BD. For ABCD to be a parallelogram, the following must be true:
Thus, the correct response is:
EB must be the same length as ED.
