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Is quadrilateral ABCD a rhombus?

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Re: Is quadrilateral ABCD a rhombus? (1) Line segments AC and BD  [#permalink]

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New post 22 Aug 2015, 11:07
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  [#permalink]

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New post 22 Aug 2015, 13:28
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?  [#permalink]

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New post 24 Feb 2017, 02:49
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?  [#permalink]

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New post 04 May 2017, 20:37
Aren't the diagonals of any parallelogram perpendicular bisectors?
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Re: Is quadrilateral ABCD a rhombus?  [#permalink]

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Re: Is quadrilateral ABCD a rhombus?  [#permalink]

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New post 03 Aug 2017, 06:59
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?  [#permalink]

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New post 12 Oct 2017, 18:59
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?  [#permalink]

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New post 10 Apr 2018, 20:32
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?  [#permalink]

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New post 10 Apr 2018, 20:40
thinkpad18 wrote:
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?


A perpendicular bisector is a line which cuts a line segment into two equal parts at 90°.

A line segment bisector is a line which cuts a line segment into two equal parts.

As for your other doubt, I think it is answered on the previous two pages:
https://gmatclub.com/forum/is-quadrilat ... ml#p999739
https://gmatclub.com/forum/is-quadrilat ... l#p1277833
https://gmatclub.com/forum/is-quadrilat ... l#p1438436
https://gmatclub.com/forum/is-quadrilat ... l#p1497287

Hope it helps.
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Is quadrilateral ABCD a rhombus?  [#permalink]

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New post 04 May 2018, 00:30
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?  [#permalink]

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New post 04 May 2018, 01:28
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?  [#permalink]

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New post 04 May 2018, 01:45
[/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?  [#permalink]

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New post 17 Jun 2018, 00:50
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?  [#permalink]

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New post 18 Jun 2018, 19:35
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
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Re: Is quadrilateral ABCD a rhombus?  [#permalink]

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New post 01 Nov 2018, 06:02
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


Bunuel, following your logic, is it true that every rectangle is parallelogram?

also if I have a square this means that it is also a rectangle, a rhombus and a parallelogram, right?
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Re: Is quadrilateral ABCD a rhombus?  [#permalink]

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New post 01 Nov 2018, 06:18
1
mrjoe1 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


Bunuel, following your logic, is it true that every rectangle is parallelogram?

also if I have a square this means that it is also a rectangle, a rhombus and a parallelogram, right?

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Re: Is quadrilateral ABCD a rhombus? &nbs [#permalink] 01 Nov 2018, 06:18

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