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Is quadrilateral ABCD a rhombus?

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Senior Manager
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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, 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 [#permalink]

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New post 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? [#permalink]

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New post 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? [#permalink]

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

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New post 05 May 2017, 02:21
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Re: Is quadrilateral ABCD a rhombus? [#permalink]

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New post 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? [#permalink]

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New post 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? [#permalink]

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New post 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? [#permalink]

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New post 10 Apr 2018, 21:40
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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Re: Is quadrilateral ABCD a rhombus?   [#permalink] 10 Apr 2018, 21:40

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