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Re: Is quadrilateral ABCD a rhombus? (1) Line segments AC and BD
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22 Aug 2015, 12:07
gijoedude wrote: Is quadrilateral ABCD a rhombus?
(1) Line segments AC and BD are perpendicular bisectors of each other.
(2) AB = BC = CD = AD
Solve! CONDITIONS 1 AND 2 APPLY TO BOTH SQUARE AND RHOMBUS............... HENCE GIVEN CONDITION 1 AND 2 , ANSWER ON WHETHER quadrilateral ABCD a rhombus IS BOTH " YES" AND "NO"...... HENCE ANSWER SHOULD BE "E".....................



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Re: Is quadrilateral ABCD a rhombus? (1) Line segments AC and BD
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22 Aug 2015, 14:28
semwal wrote: gijoedude wrote: Is quadrilateral ABCD a rhombus?
(1) Line segments AC and BD are perpendicular bisectors of each other.
(2) AB = BC = CD = AD
Solve! CONDITIONS 1 AND 2 APPLY TO BOTH SQUARE AND RHOMBUS............... HENCE GIVEN CONDITION 1 AND 2 , ANSWER ON WHETHER quadrilateral ABCD a rhombus IS BOTH " YES" AND "NO"...... HENCE ANSWER SHOULD BE "E"..................... As mentioned in posts above, a square is a special type of rhombus and hence both statements are sufficient on their own, making C the correct answer.



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Re: Is quadrilateral ABCD a rhombus?
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24 Feb 2017, 03:49
Superset The answer to the question will be either yes or no.
Translation In order to find the answer, we need: 1# measure of length of sides 2# angle between the diagonals 3# other properties to justify that the quadrilateral is a triangle
Statement analysis St 1: diagonals are bisectors happens in parallelogram. Diagonals are perpendicular happens in kite. A figure common to both is a rhombus. ANSWER.
St 2: if all sides are equal. The figure will be a rhombus. ANSWER
Option D



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Re: Is quadrilateral ABCD a rhombus?
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04 May 2017, 21:37
Aren't the diagonals of any parallelogram perpendicular bisectors?



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Re: Is quadrilateral ABCD a rhombus?
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05 May 2017, 02:21



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Re: Is quadrilateral ABCD a rhombus?
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03 Aug 2017, 07:59
Stmnt 1) Satisfied only in rhombus and square, and square is special type of rhombus
Statement 2) Even this statement is Satisfied only in rhombus and square, and square is special type of rhombus



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Re: Is quadrilateral ABCD a rhombus?
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12 Oct 2017, 19:59
Economist wrote: Is quadrilateral ABCD a rhombus?
(1) Line segments AC and BD are perpendicular bisectors of each other.
(2) AB = BC = CD = AD All Squares > Rhombuses However not all Rhombuses are squares Four equal sides > square If A then B does not imply If B then A Perpendicular Bisectors > Rhombus Statement 1 Suff Statement 2 Suff D



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Re: Is quadrilateral ABCD a rhombus?
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10 Apr 2018, 21:32
Bunuel wrote: Answer D.
(1) Line segments AC and BD are perpendicular bisectors of each other. > rhombus
(2) AB = BC = CD = AD > rhombus
Or am I missing something, seems pretty obvious... Hi Bunuel, Thanks for all your help. I have a question. Why is statement 1 a rhombus and not a kite or square? I am guessing it has to do with intersecting at 90 degrees vs. perpendicular bisectors. What is the difference between the two terminologies?



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Re: Is quadrilateral ABCD a rhombus?
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10 Apr 2018, 21:40



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Is quadrilateral ABCD a rhombus?
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04 May 2018, 01:30
VeritasPrepKarishma wrote: TooLong150 wrote: This question is poor, because (1) could be right kite, which is not necessarily a rhombus or a rhombus, but (2) will always satisfy a rhombus. Actually, the question is fine. A rhombus is a quadrilateral all of whose sides are of the same length  that's all. You could have a rhombus which also has all angles 90 which makes it a square or a rhombus in the shape of a kite. But nevertheless, if it is a quadrilateral and has all sides equal, it IS A RHOMBUS. (1) Line segments AC and BD are perpendicular bisectors of each other. Make 2 lines  a vertical and a horizontal  which are perpendicular bisectors of each other. Make them in any way of any length  just that they should be perpendicular bisectors of each other. When you join the end points, you will get all sides equal. Think of it this way  each side you get will be a hypotenuse of a right triangle. The legs of the right triangle will have the same pair of lengths in all 4 cases. So AB = BC = CD = AD. So ABCD must be a rhombus. (2) AB = BC = CD = AD This statement directly tells you that all sides are equal so ABCD must be a rhombus. Answer (D) I am confused here. For me the answer would be A. In case of the B, all sides are equal, yes but how do we know that opposite sides are parallel as well  all sides equal and opposite sides parallel is a rhombus, isn't it?



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Re: Is quadrilateral ABCD a rhombus?
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04 May 2018, 02:28
vipashyana wrote: VeritasPrepKarishma wrote: TooLong150 wrote: This question is poor, because (1) could be right kite, which is not necessarily a rhombus or a rhombus, but (2) will always satisfy a rhombus. Actually, the question is fine. A rhombus is a quadrilateral all of whose sides are of the same length  that's all. You could have a rhombus which also has all angles 90 which makes it a square or a rhombus in the shape of a kite. But nevertheless, if it is a quadrilateral and has all sides equal, it IS A RHOMBUS. (1) Line segments AC and BD are perpendicular bisectors of each other. Make 2 lines  a vertical and a horizontal  which are perpendicular bisectors of each other. Make them in any way of any length  just that they should be perpendicular bisectors of each other. When you join the end points, you will get all sides equal. Think of it this way  each side you get will be a hypotenuse of a right triangle. The legs of the right triangle will have the same pair of lengths in all 4 cases. So AB = BC = CD = AD. So ABCD must be a rhombus. (2) AB = BC = CD = AD This statement directly tells you that all sides are equal so ABCD must be a rhombus. Answer (D) I am confused here. For me the answer would be A. In case of the B, all sides are equal, yes but how do we know that opposite sides are parallel as well  all sides equal and opposite sides parallel is a rhombus, isn't it? hello If you draw a quadrilateral with all sides equal, then its opposite sides HAVE to be parallel.



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Re: Is quadrilateral ABCD a rhombus?
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04 May 2018, 02:45
[/quote]
I am confused here. For me the answer would be A. In case of the B, all sides are equal, yes but how do we know that opposite sides are parallel as well  all sides equal and opposite sides parallel is a rhombus, isn't it?[/quote]
hello
If you draw a quadrilateral with all sides equal, then its opposite sides HAVE to be parallel.[/quote]
Agreed. Sorry, my bad.



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Re: Is quadrilateral ABCD a rhombus?
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17 Jun 2018, 01:50
Bunuel wrote: Thought about this again: D it is.
Well: (1) True for square or for rhombus but every square is a rhombus, so sufficient (2) Again true for square or for rhombus but every square is a rhombus, so sufficient
D Just one question if you could help me. Are not diagonals of rectangle perpendicular bisectors of each other. I know that they are not equal but they are at 90 degrees to each other and divide the diagonals in equal halves.



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Re: Is quadrilateral ABCD a rhombus?
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18 Jun 2018, 20:35
manishk30 wrote: Bunuel wrote: Thought about this again: D it is.
Well: (1) True for square or for rhombus but every square is a rhombus, so sufficient (2) Again true for square or for rhombus but every square is a rhombus, so sufficient
D Just one question if you could help me. Are not diagonals of rectangle perpendicular bisectors of each other. I know that they are not equal but they are at 90 degrees to each other and divide the diagonals in equal halves. Hello Diagonals of a rectangle ARE EQUAL and ARE bisectors of each other, but they are NOT necessarily perpendicular bisectors. A rectangle in which diagonals intersect at perpendicular (90 degrees) becomes a square




Re: Is quadrilateral ABCD a rhombus? &nbs
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