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Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect

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Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink] New post 23 Jul 2010, 05:03
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Is ABCD a rhombus?

(1) ABCD is a square
(2) ABCD diagonals bisect at 90 degrees
[Reveal] Spoiler: OA

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Re: Quadrlateral DS [#permalink] New post 23 Jul 2010, 05:13
c
both r the properties of rhombus
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Re: Quadrlateral DS [#permalink] New post 23 Jul 2010, 05:16
I go with option A.. Square is a rhombus with all angles equal.. For option B, it doesn't mention about the parallel line prop.

Share the answer pls.

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Re: Quadrlateral DS [#permalink] New post 23 Jul 2010, 06:23
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Answer is D.

Statement 1 says that ABCD is a square. A square is just a special rhombus with all angles equal to 90^o

Statement 2: Diagonals bisect at 90^o

Let's draw a picture to visualize this:
Attachment:
c73058.jpg
c73058.jpg [ 10.66 KiB | Viewed 2029 times ]
(Let's consider the center point to be O, I forgot to label this)

So as you can see from the image, since the diagonals are bisected, we have AO = OC. And we have OB to be common for triangles AOB and BOC. So consider right triangle AOB:
AB^2 = AO^2 + OB ^2 = OC^2 + OB^2 = BC^2.

So we get that AB = BC. Similarly we can prove that all the sides are equal using this method. Hence we get a quadrilateral where all sides are equal, and diagonals bisecting at 90^o. Hence it's a rhombus. Sufficient.
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Re: Quadrlateral DS [#permalink] New post 10 Mar 2013, 15:43
whiplash2411 wrote:
Answer is D.

Statement 1 says that ABCD is a square. A square is just a special rhombus with all angles equal to 90^o

Statement 2: Diagonals bisect at 90^o

Let's draw a picture to visualize this:
Attachment:
c73058.jpg
(Let's consider the center point to be O, I forgot to label this)

So as you can see from the image, since the diagonals are bisected, we have AO = OC. And we have OB to be common for triangles AOB and BOC. So consider right triangle AOB:
AB^2 = AO^2 + OB ^2 = OC^2 + OB^2 = BC^2.

So we get that AB = BC. Similarly we can prove that all the sides are equal using this method. Hence we get a quadrilateral where all sides are equal, and diagonals bisecting at 90^o. Hence it's a rhombus. Sufficient.



Hey whiplash2411,
I agree A is Correct choice..
But not D!
I don't think B also leads to solution here..
B just says bisect each other. It doesn't mean that both should be of equal length!

Guys pls correct me if im wrong
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Re: Quadrlateral DS [#permalink] New post 10 Mar 2013, 21:43
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shanmugamgsn wrote:
whiplash2411 wrote:
Answer is D.

Statement 1 says that ABCD is a square. A square is just a special rhombus with all angles equal to 90^o

Statement 2: Diagonals bisect at 90^o

Let's draw a picture to visualize this:
Attachment:
c73058.jpg
(Let's consider the center point to be O, I forgot to label this)

So as you can see from the image, since the diagonals are bisected, we have AO = OC. And we have OB to be common for triangles AOB and BOC. So consider right triangle AOB:
AB^2 = AO^2 + OB ^2 = OC^2 + OB^2 = BC^2.

So we get that AB = BC. Similarly we can prove that all the sides are equal using this method. Hence we get a quadrilateral where all sides are equal, and diagonals bisecting at 90^o. Hence it's a rhombus. Sufficient.



Hey whiplash2411,
I agree A is Correct choice..
But not D!
I don't think B also leads to solution here..
B just says bisect each other. It doesn't mean that both should be of equal length!

Guys pls correct me if im wrong


If the diagonals of a quadrilateral are perpendicular bisectors of each other (so if the diagonal bisect each other at a right angle), the quadrilateral is a rhombus.
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Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink] New post 12 Mar 2013, 20:28
I believe the answer here is A.
What is rombus - it is quadrilateral with the following properties:
* Opposite angles of a rhombus have equal measure
* The two diagonals of a rhombus are perpendicular;
* Its diagonals bisect opposite angles (that is why we have first property)
In choice B we do not see all the properties, it could be a rombus but at the same time it could be an quadrilateral with different angles and opposite sides - not sufficient.
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Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink] New post 13 Mar 2013, 02:37
Expert's post
ziko wrote:
I believe the answer here is A.
What is rombus - it is quadrilateral with the following properties:
* Opposite angles of a rhombus have equal measure
* The two diagonals of a rhombus are perpendicular;
* Its diagonals bisect opposite angles (that is why we have first property)
In choice B we do not see all the properties, it could be a rombus but at the same time it could be an quadrilateral with different angles and opposite sides - not sufficient.


OA is D, not A.

There is a property which says if the diagonals of a quadrilateral are perpendicular bisectors of each other (so if the diagonal bisect each other at a right angle), the quadrilateral is a rhombus.
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Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink] New post 13 Mar 2013, 22:17
Bunuel wrote:
ziko wrote:
I believe the answer here is A.
What is rombus - it is quadrilateral with the following properties:
* Opposite angles of a rhombus have equal measure
* The two diagonals of a rhombus are perpendicular;
* Its diagonals bisect opposite angles (that is why we have first property)
In choice B we do not see all the properties, it could be a rombus but at the same time it could be an quadrilateral with different angles and opposite sides - not sufficient.


OA is D, not A.

There is a property which says if the diagonals of a quadrilateral are perpendicular bisectors of each other (so if the diagonal bisect each other at a right angle), the quadrilateral is a rhombus.


Most probably i missed the word bisects, which means divides into equal sides, and understood it as intersects. In this case obviously that will be a rombus and no other figure could be drawn. Yes once again i confirm that GMAT has so many small tricky parts.
Thank you Bunuel for clarification.
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Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink] New post 06 Aug 2013, 10:15
The answer is D.
All Square are Rombus, so first is that A Satisfies the condition.

Now, if any two diagonals bisects each other, then also it will always be rombus, so B also satisfies the condition.

Since both A and B alone satisfies the condition the answer is D
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Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink] New post 06 Aug 2013, 11:06
rxs0005 wrote:
Is ABCD a rhombus?

(1) ABCD is a square
(2) ABCD diagonals bisect at 90 degrees


D

Rule for Rhombus:
Diagonals should bisect each other and angle between diagonals should be 90degrees.
If all sides of a Rhombus are equal then it is a square.

Any square is a Rhombus
If the diagonal bisects at 90 degrees then it is a Rhombus.

So either of the statement alone is sufficient to answer the question.
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Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect   [#permalink] 06 Aug 2013, 11:06
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