M14, Q32 : quadrilateral : Retired Discussions [Locked] - Page 2
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24 Jun 2013, 06:59
Moss wrote:
Its not stated that the shape is a parallelogram, so the shape could be something like a trapezoid. Knowing something about two of the interior angles doesn't tell us anything about the rest, and we therefore do not know anything about the lengths of the diagonals; 1 does not hold.

Based on 2, we know that the shape must be a rhombus, but we don't know anything about the interior angles; 2 does not hold.

Together, we know that the same is a rhombus and which of the angles are large/small -- we can therefore answer the question; C.

Nice explanation! Thanks:)
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24 Jun 2013, 08:32
Rephrasing the question stem.

Is the diagonal D1 grater than the Diagonal D2
yes / no question

rephrasing statement A) the quadrilateral is not a square or Rectangle, it could be a parallelogram, trapezoid or rhombus. since a parallelogram or trapezoid depending on the length can have equal diagonals this statement is not sufficient

rephrasing statement B) the quadrilateral is a square or a rhombus. if the quadrilateral is a square, the diagonals are of equal length, if the quadrilateral is a rhombus then the diagonals are of different length. hence the statement by itself is not sufficient.

taking together both statements A and B the quadrilateral is a rhombus and hence diagonals are of varied length. the correct answer choice is C) statement A and B together
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24 Jun 2013, 10:06

i) Insufficient - The angles don't say anything about the diagonals or the side in this case.
ii) Insufficient - All sides equal means, the quadrilateral is either a square or a rhombus.
- A square has equal sides and the diagonals are equal
- A rhombus has equal sides but does not have equal diagonals.

C) - Both combined together you know, one of the angles is greater than the other, hence one diagonal is greater than the other.
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03 Jun 2014, 01:39
Can someone please explain how we decide that third side must be greater if opposite angle is greater when other two sides are equal?
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