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 a different length than EB.¯¯¯¯¯¯¯¯¯
ED ¯¯¯¯¯¯¯¯¯ must be a different length than EB.¯¯¯¯¯¯¯¯¯
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¯¯¯¯¯¯¯¯.
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1 answer
To prove that quadrilateral ABCD is a parallelogram using the diagonals that intersect at point E, you would need to demonstrate that the segments formed by the intersection point E on the diagonals are proportional.
In a parallelogram, the diagonals bisect each other, which means that:
\[ EB = ED \]
This implies that the lengths of segments EB and ED must be equal.
Therefore, the correct response is:
EB must be the same length as ED.
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