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joshi.komal
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 Posted: Tue Jan 22, 2008 5:56 am Post subject: Why the answer is D |
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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 |
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sankruth
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| Posted: Tue Jan 22, 2008 6:06 am Post subject: |
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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! |
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Stuart Kovinsky
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| Posted: Tue Jan 22, 2008 6:33 am Post subject: |
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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.
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Last edited by Stuart Kovinsky on Wed Jan 23, 2008 12:13 pm; edited 1 time in total |
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preciousrain7
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| Posted: Wed Jan 23, 2008 11:47 am Post subject: |
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| 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. |
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 |
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Stuart Kovinsky
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| Posted: Wed Jan 23, 2008 12:12 pm Post subject: |
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| preciousrain7 wrote: | | 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. |
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 |
Not quite. Here's what we can say:
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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preciousrain7
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| Posted: Wed Jan 23, 2008 2:25 pm Post subject: |
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| 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 |
Not quite. Here's what we can say:
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. |
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