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Is quadrilateral ABCD a rhombus?

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honchos
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Is quadrilateral ABCD a rhombus? [#permalink] New post   Updated on: 20 Dec 2014, 08:26
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Is quadrilateral ABCD a rhombus?

(1) AC is perpendicular to BD
(2) AB + CD = BC +AD

M11-05

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E

Originally posted by honchos on 20 Dec 2014, 02:30.
Last edited by Bunuel on 20 Dec 2014, 08:26, edited 1 time in total.
Edited the question.
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Re: Is quadrilateral ABCD a rhombus? [#permalink] New post   20 Dec 2014, 08:26
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Is quadrilateral \(ABCD\) a rhombus?

(1) \(AC\) is perpendicular to \(BD\).

This property holds true for both rhombi and kites, so this information alone is not sufficient to determine whether \(ABCD\) is a rhombus.

(2) \(AB + CD = BC + AD\).

This property is also true for both rhombi and kites, so this information alone is not sufficient to determine whether \(ABCD\) is a rhombus.

(1)+(2) Combining the two statements does not provide any additional information. Quadrilateral \(ABCD\) could still be either a rhombus or a kite. Not sufficient.

Refer to the image below for visualization:




Answer: E
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Kite and Rhombus.png
Kite and Rhombus.png [ 167.86 KiB | Viewed 17874 times ]

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Re: Is quadrilateral ABCD a rhombus? [#permalink] New post   16 May 2017, 02:35
(1) Line segments AC and BD are perpendicular bisectors of each other.

Perpendicular bisector means it would divide the line into half and thus the quadrilateral formed by joining A,B,C,D will have equal side and that is the property of rhombus
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Re: Is quadrilateral ABCD a rhombus? [#permalink] New post   18 May 2017, 08:20
23a2012 wrote:
Why the above question has the answer E while the below question has the answer D?Where I can understand the difference between option B in the both question from Bunuel clarification but I did not see any difference in the option A between both qouestion so why option A is incorrect in the above question while it is correct in the below question?

Is quadrilateral ABCD a rhombus?

(1) Line segments AC and BD are perpendicular bisectors of each other.

(2) AB = BC = CD = AD


In the Kite as Bunuel explained notice that only one diagonal is bisected while the other is not while in rhombus/square both diagonals are bisected(since, square is a special case of rhombus). So, (1) is sufficient. As far (2) is concerned it has to be rhombus any quadrilateral having equal sides is a rhombus & hence, (2) is sufficient as well.
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Re: Is quadrilateral ABCD a rhombus? [#permalink] New post   06 Sep 2017, 22:28
honchos wrote:
Is quadrilateral ABCD a rhombus?

(1) AC is perpendicular to BD
(2) AB + CD = BC +AD

M11-05


Statement 1

No because this could simply be a rectangle- a rectangle in which the lengths are bigger than the widths

Insuff

Statement 2

Actually no- this statement is trying to trick you into assuming that all four sides are equal, in which case the statement would be sufficient. However, a kite can fit this criteria and so

Insuff
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Re: Is quadrilateral ABCD a rhombus? [#permalink] New post   12 Oct 2017, 20:03
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honchos wrote:
Is quadrilateral ABCD a rhombus?

(1) AC is perpendicular to BD
(2) AB + CD = BC +AD

M11-05


Bunuel what what is the difference between saying "AC is perpendicular to BD" v "AC and BD are perpendicular bisectors"

In other problems the statement is a rhombus if it is known that "AC and BD are perpendicular bisectors."
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Re: Is quadrilateral ABCD a rhombus? [#permalink] New post   12 Oct 2017, 20:50
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Nunuboy1994 wrote:
honchos wrote:
Is quadrilateral ABCD a rhombus?

(1) AC is perpendicular to BD
(2) AB + CD = BC +AD

M11-05


Bunuel what what is the difference between saying "AC is perpendicular to BD" v "AC and BD are perpendicular bisectors"

In other problems the statement is a rhombus if it is known that "AC and BD are perpendicular bisectors."



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.

A line is perpendicular to another if it meets or crosses it at right angles (90°).
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Re: Is quadrilateral ABCD a rhombus? [#permalink] New post   15 Jun 2023, 01:48
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Re: Is quadrilateral ABCD a rhombus? [#permalink]
15 Jun 2023, 01:48
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