Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o

Question

Is Quadrilateral ABCD a Rectangle?

1) Diagonals of ABCD Bisect each other at 90 degrees
2) Diagonals of ABCD are equal in dimension

Source:  https://www.GMATInsight.com

Bunuel · Answer

chetan2u · Answer

Main statement tells us that ABCD is a Quadrilateral..

Let's see the statements..

1) Diagonals of ABCD Bisect each other at 90 degrees
 this tells us that the diagonals cut each other at middle of each other at 90°
The diagonals can be of different sizes..
So it is surely a RHOMBUS but cannot say if it is rectangle/square 
Insufficient

2) Diagonals of ABCD are equal in dimension
Diagonals are equal cannot alone suffice if it's a rectangle..

Combined..
It is a rhombus from statement I and diagonals are EQUAL from statement II..
It is a square and each square is also a rectangle..
Sufficient 
C

gmatexam439 · Answer

Hello  chetan2u  /  Bunuel ,
How do we distinguish when to treat a square as A SQUARE and not a rectangle.
It's true all squares are rectangles. I did reach at the conclusion that from both A and B the quadrilateral is a square. But marked "E".
Regards

mohshu · Answer

hi  chetan2u  ...

stat2 states diagnols are equal...in a quadrialteral, only square and rectangle have equal diagnols,,,
i cant think of any other figure where diagnols ar equal
please help

chetan2u · Answer

Hi,

Surely if diagonals are EQUAL and BISECT each other, it would be rectangle or square..
But here it is just diagonals are EQUAL. Say both are 5 m but they bisect at 1 m from top, it will not be rectangle or square..
Once you draw, you will see various Quadrilateral can be made .

stonecold · Answer

Here is an example -->

Check out this trapezoid with equal diagonals

https://www.mathwarehouse.com/geometry/quadrilaterals/trapezoid/isosceles/diag/picture.jpg

It clearly isn't a rectangle

mohshu · Answer

ok..makes sense now,,,,thanks

i guess that shud be intersect??? bisect means dividing each other into two equal parts...
correct me if im rong,,
thanks

MrJglass · Answer

Statement1 is not surely a rhombus. The diagonals of a kite are also perpendicular to each other.

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vivapopo · Answer

.

I think there is a difference between "bisect" and "intersect"
 In a quadrilateral, if diagonals intersect each other at 90 degrees, then it could be a rhombus or a square or a kite. In first two cases we can call it a rhombus only (because square is a special kind of rhombus) but if its a kite, it cannot be called a rhombus. . 
(Please note that the statement does NOT say 'intersect each other at 90' but it says bisect each other at 90'.
Diagonals of a square, a rectangle and an isosceles trapezoid are equal in dimension. In the first case (if its a square) we can call it a rhombus (square is a special kind of rhombus) but in other two cases we cannot.

Hero8888 · Answer

Hi  chetan2u

Please correct me if I'm wrong. I'm attaching a file with a figure in which diagonals are equal and cross at 90 degree yet the figure is a kite, not a parallelogram.

chetan2u · Answer

Yes, it is not a parallelogram.
The reason is that the diagonals have to be equal and bisect each other and if you do the same here, it will become a rhombus

Hero8888 · Answer

Hi  chetan2u

Please correct me if I'm wrong. I'm attaching a file with a figure in which diagonals are equal and cross at 90 degree yet the figure is a kite, not a parallelogram.

Yes, it is not a parallelogram.
The reason is that the diagonals have to be equal and bisect each other and if you do the same here, it will become a rhombus

Sorry, I meant Rectangle. So the OA has to be E?

chetan2u · Answer

Yes, it is not a parallelogram.
The reason is that the diagonals have to be equal and bisect each other and if you do the same here, it will become a rhombus

Sorry, I meant Rectangle. So the OA has to be E.

NO, the OA will be C.

you have not read the complete info of statement I.
1) Diagonals of ABCD Bisect each other at 90 degrees
so statement I tells us that the diagonals bisect each other. Bisect means they intersect at the centre.

so combined it has to be a rectangle - equal diagonals and bisecting each other at 90 would be a square and square is also a rectangle

ranjitmkunte · Answer

Why statement 1 alone is not sufficient??
Diagonals of a rectangle do not bisect at 90 deg. So statement 1 should be sufficient to decide that its not a rectangle but any other quadrilateral (may be a square)
Please help.

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chetan2u · Answer

A square is always a rectangle, although it may not be necessary that a rectangle is a square.

abhishekmayank · Answer

Bunuel ,  GMATinsight 
 Should not the answer be E, as both Rhombus and Square satisfy both the conditions of 1 and 2 ?

GMATinsight · Answer

abhishekmayank

After combining the statements, we get only a square (which is a rhombus too but is also a rectangle) hence Sufficient

You can't get any rhombus that is not a square after combining the two statements

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Is Quadrilateral ABCD a Rectangle? 1) Diagonals of ABCD Bisect each o

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