Is quadrilateral ABCD a parallelogram ?

Question

1) Two sides measure 8 cm in length while the other two sides measure 6 cm in length.

2) AC is perpendicular to BD.

AMITAGARWAL2 · Answer

I think answer should be E. What if it is a kite type of shape. Then it is not a parallelogram but still meets the both criteria. I would wait for experts to comment..

innocous · Answer

IMO as u say mate kite meets both the criterion and it is not a parallelogram therefore we are getting a definite answer 
to with combining as "C" ...by combining the two information we are getting definite answer as NO "it is not a parallelogram" because it will be a kite which is NOT a parallelogram...

plz give kudos if it was a help..

AMITAGARWAL2 · Answer

but with the current information it could be a rectangle, which is a rectangle and rectangle is a parallogram too. right?

blueseas · Answer

diagonals of RECTANGLE are not perpedicular,so in this case it cannot be rectangle.

diagonals are perpendicular only for SQUARE/RHOMBUS/KITE.

hope it helps

abhijeetjha · Answer

Statement 1 leads us to a parallelogram or a rectangle in which opposite sides are equal or to a Kite in which adjacent sides are equal ..thus all these quadrilaterals meet the criteria of st 1...Thus as we cant get a definite shape its insufficient..

Statement 2 leads us to a square , a rhombus or a kite....as diagonals of these three shapes intersect at right angle...so again no definite data and its insufficient..

Combining these two we can clearly infer that the figure is a kite ...OR its not a parallelogram for sure ....So we are getting a definite answer combining two statements ..Thus C...

mdacosta · Answer

can someone please elaborate why a parallelogram does not fit both 1 & 2? I understand the kite part, but have a little confusion on the other.

Thanks!

AbhinavBankhwal · Answer

why cannot the answer be B

Statement 2 says that the diagonals are perpendicular, which means the figure can either be a square/rhombus/kite. This confirms that it is NOT A PARALLELOGRAM. A definite answer.

Have I missed something?

Thanks.

rekhabishop · Answer

I agree! The answer should be B. chetan2u and Bunuel could you please help us out with this question?

darn · Answer

Every square and Rhombus is a parallelogram

A parallelogram is a quadrilateral with 2 pairs of parallel sides. 
The opposite sides on every square and on every rhombus are parallel, so every square and rhombus is a parallelogram.

ccooley · Answer

Statement 1:

https://i.imgur.com/rGPust9.png

Statement 2:

https://i.imgur.com/LCMjhjb.png

Statements 1 and 2 together:

This is where it gets really interesting. We know the diagonals are perpendicular, and the four sides are 8, 8, 6, and 6.

There are only two possible ways to arrange the sides. Either the opposite sides are equal, like this:

https://i.imgur.com/yoGODLz.png

Or the adjacent sides are equal, like this:

https://i.imgur.com/vkjl3wo.png

However,  if the opposite sides are equal, the two diagonals can't be perpendicular.

Here's the simplest argument I could come up with to demonstrate that:

https://i.imgur.com/t7R2Mgo.png

The diagonals of a parallelogram should split each other in half. If they're perpendicular (have a right angle between them), we should be able to use right triangle rules! So, x^2 + y^2 = 6^2. However, we also have x^2 + y^2 = 8^2. It's impossible for the same equation to have two different values like that - so, it's logically impossible for the diagonals to be perpendicular.

In other words, if the opposite sides are equal, Statement 2 can't also be true. It's mathematically impossible. But Statement 2  has  to be true, since we're combining the two statements together.

The only possible way to combine the two statements together and have them both be true, is if the adjacent sides are equal. This shape is the only possible one that fits both statements:

https://i.imgur.com/vkjl3wo.png

This shape is  not  a parallelogram. So, we can definitively answer 'no' to the question.  The correct answer is C .

Nunuboy1994 · Answer

ccooley and Bunuel This question https://gmatclub.com/forum/is-abcd-a-ro ... l#p1921432 States that if we know that a quadrilatral has perpendicular bisectors, two diagonals that bisect at 90, the we have enough to know that the figure is a rhombus? And if we know that the figure is a rhombus then we also know that the figure is a paralleogram? Kudos for explanation.

Nunuboy1994 · Answer

ccooley https://gmatclub.com/forum/is-quadrilat ... 85336.html This question also states that if we know that the diagonals of a quadrilateral are perpendicular bisectors of each other then we know for sure that the figure is a rhombus? And because a parallelogram is a broader category then wouldn't the figure have to be a parallelogram? What is the difference between the diagonals of a four sided figure being perpendicular to each other vs being perpendicular bisectors ? Kudos

Nunuboy1994 · Answer

ccooley and Bunuel https://gmatclub.com/forum/is-quadrilat ... 45937.html This question too- could please explain the difference between simply perpendicular diagonals and diagonals that are perpendicular bisectors?

Bunuel · Answer

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°).

hellosanthosh2k2 · Answer

Answer cannot be B. A rhombus and a kite has perpendicular diagonals. A rhombus is a parallelogram, but kite is not.

Combining 1 and 2, the given figure can't be rhombus(parallelogram), because we have unequal sides. so it must be kite and not a rhombus(parallelogram).

Answer (C)

omkartadsare · Answer

1) Two sides measure 8 cm in length while the other two sides measure 6 cm in length.
2) AC is perpendicular to BD.

from (1). it can be a kite or a paralellogram. 
 (2). it can be a kite or a square or a rhombus (for a parallelogram to have digonals intersect at 90, 
 all sides have to be same)

Combined, its clear that its not a square/rhombus. Hence it is a kite. Hence (C)

djmobley · Answer

Statement 1:tells us this is not a square. So it could be a rectangle or rhombus. Two answers - not suff.

Statement 2: Thing to know here: Perpendicular diagonals only apply to a square or a rhombus - not rectangles. So this could now be a rhombus or a square.Two answers - not suff.

Putting them together rules out both squares and rectangles. This must be a rhombus. Idc what a rhombus is in terms of data suff. All I know is I narrowed this *complain* down to one possibility - who cares if it's a parallelogram or not.

bumpbot · Answer

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Is quadrilateral ABCD a parallelogram ?

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