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24 Jun 2022, 10:24
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Difficulty:
45%
(medium)
Question Stats:
56% (00:58) correct
44%
(00:48)
wrong
based on 50
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In the figure above, is AB || CD?
(1) AB = CD
(2) AD = BC
25 Jun 2022, 17:56
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Definition of a Parallelogram:
a four sided convex polygon with both pairs of opposite sides parallel
Property of Parallelogram: both pairs of opposite sides are of Equal Length
The CONVERSE of the Property works to prove the figure a parallelogram—— For any given quadrilateral, if both pairs of opposite sides are equal, the quadrilateral must be a parallelogram (and hence both pairs of opposite sides are parallel)
Each statement alone provides us with a quadrilateral with just one pair of opposite sides equal.
Statement 1: the figure could be an isosceles trapezoid with AB = CD as the non parallel, but equal sides.
Or the figure could be a parallelogram.
Statement 2: the figure could be any number of irregular quadrilateral in which AB = CD (opposite sides) are equal, but positioned in such a way that they are facing each other at different angles (the length of the other pair of opposite sides differs).
Or it could be a parallelogram.
Neither statement is sufficient alone.
However, using the statements together, the figure must be a parallelogram since both pairs of opposite sides are equal.
C
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a four sided convex polygon with both pairs of opposite sides parallel
Property of Parallelogram: both pairs of opposite sides are of Equal Length
The CONVERSE of the Property works to prove the figure a parallelogram—— For any given quadrilateral, if both pairs of opposite sides are equal, the quadrilateral must be a parallelogram (and hence both pairs of opposite sides are parallel)
Each statement alone provides us with a quadrilateral with just one pair of opposite sides equal.
Statement 1: the figure could be an isosceles trapezoid with AB = CD as the non parallel, but equal sides.
Or the figure could be a parallelogram.
Statement 2: the figure could be any number of irregular quadrilateral in which AB = CD (opposite sides) are equal, but positioned in such a way that they are facing each other at different angles (the length of the other pair of opposite sides differs).
Or it could be a parallelogram.
Neither statement is sufficient alone.
However, using the statements together, the figure must be a parallelogram since both pairs of opposite sides are equal.
C
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26 Jun 2022, 00:53
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(1) Not sufficient.
(2) Not Sufficient.
(1)+(2) The opposite sides are equal. So the quadrilateral must be at least a parallelogram.
Opposite sides of parallelogram are parallel to each other.
Combining the two statements is sufficient.
Answer: C
(2) Not Sufficient.
(1)+(2) The opposite sides are equal. So the quadrilateral must be at least a parallelogram.
Opposite sides of parallelogram are parallel to each other.
Combining the two statements is sufficient.
Answer: C
