Is quadrilateral ABCD a rhombus?
(1) Line segments AC and BD are perpendicular bisectors of each other.
(2) AB = BC = CD = AD
I am not sure why stmt 2 is sufficient... Can anyone explain
Thanks
Komal
Why the answer is D
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St 1: SUFF
If diagonals are perpendicular bisectors of each other then fugure is a Square or Rhombus.
St2 : SUFF
If 4 sides are equal, then figure must be a square or rhombus. Square is Rhombus where both diagonals have equal length and are perpendicular bisectors of each other
So, D. Hope that helps!
If diagonals are perpendicular bisectors of each other then fugure is a Square or Rhombus.
St2 : SUFF
If 4 sides are equal, then figure must be a square or rhombus. Square is Rhombus where both diagonals have equal length and are perpendicular bisectors of each other
So, D. Hope that helps!
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A rhombus is a parallelogram with 4 equal sides. A square is just a special kind of rhombus (just like a square is a special kind of rectangle).
So, if we have a 4 sided shape with equal sides, it falls within the definition of a rhombus.
So, if we have a 4 sided shape with equal sides, it falls within the definition of a rhombus.
Last edited by Stuart@KaplanGMAT on Wed Jan 23, 2008 12:13 pm, edited 1 time in total.
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Stuart,Stuart Kovinsky wrote:A rhombus is a parallelogram with 4 equal sides. A square is just a special kind of rhombus (just like a square/rhombus is a special kind of rectangle).
So, if we have a 4 sided shape with equal sides, it falls within the definition of a rhombus.
is it safe to say, a sq can be a rhombus but a rhombus can't be a square and a sq./rhombus can be a rectangle but a rect. can't be a sq./rhombus?
Sonia
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Not quite. Here's what we can say:preciousrain7 wrote:Stuart,Stuart Kovinsky wrote:A rhombus is a parallelogram with 4 equal sides. A square is just a special kind of rhombus (just like a square is a special kind of rectangle).
So, if we have a 4 sided shape with equal sides, it falls within the definition of a rhombus.
is it safe to say, a sq can be a rhombus but a rhombus can't be a square and a sq./rhombus can be a rectangle but a rect. can't be a sq./rhombus?
Sonia
A square IS a rhombus.
A rhombus MAY BE a square.
A square IS a rectangle.
A rectangle MAY BE a square.
(I misstated the rhombus/rectangle relationship in my original post and have edited it - a rhombus isn't a rectangle, since all rectangles have 4 * 90 degree angles; a rectangle can be a rhombus, but only if it's also a square.)
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Not quite. Here's what we can say:Stuart Kovinsky wrote:
Stuart,
is it safe to say, a sq can be a rhombus but a rhombus can't be a square and a sq./rhombus can be a rectangle but a rect. can't be a sq./rhombus?
Sonia
A square IS a rhombus.
A rhombus MAY BE a square.
A square IS a rectangle.
A rectangle MAY BE a square.
(I misstated the rhombus/rectangle relationship in my original post and have edited it - a rhombus isn't a rectangle, since all rectangles have 4 * 90 degree angles; a rectangle can be a rhombus, but only if it's also a square.)[/quote]
Thank you.