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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 [ 10.66 KiB | Viewed 2073 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.

Re: Quadrlateral DS [#permalink]
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 _________________

GMAT - Practice, Patience, Persistence Kudos if u like

Re: Quadrlateral DS [#permalink]
10 Mar 2013, 21:43

1

This post received KUDOS

Expert's post

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. _________________

Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink]
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. _________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink]
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. _________________

Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink]
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. _________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect [#permalink]
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. _________________

"Hit KUDOS if you like my explanation"

gmatclubot

Re: Is ABCD a Rombus 1 ABCD is a Square 2. ABCD diagonals bisect
[#permalink]
06 Aug 2013, 11:06