Is quadrilateral ABCD a rectangle? (1) Two opposite sides of ABCD are

Question

Is quadrilateral ABCD a rectangle?

(1) Two opposite sides of ABCD are equal in length.
(2) Two opposite internal angles of ABCD are right angles.

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Bunuel · Accepted Answer

Kyala1Jameson · Answer

Is quadrilateral ABCD a rectangle?

(1) Two opposite sides of ABCD are equal in length. 
It can be rhombus or rectangle .. So not sufficient 
(2) Two opposite internal angles of ABCD are right angles.
It will be a rectangle or square .. So  sufficient  ..

Ans is B ?

twobagels · Answer

A quadrilateral is a square when it's got 4 - 90* angles and all four sides are the same length.

Neither of the 2 statements alone is sufficient to answer the question and neither are the two statements together.

From statement A, 2 sides are the same length.
From statement B, if two opposite corners are 90, all internal angles are 90.

This could be a square, which is a special case of a rectangle.

TarunKumar1234 · Answer

Is quadrilateral ABCD a rectangle?

stat1: Two opposite sides of ABCD are equal in length.
It can be parallelogram as well. Not sufficient.

Stat2: Two opposite internal angles of ABCD are right angles.
It can be Rectangle or kite. So, Not Sufficient.

Combining both, it will be a rectangle. So, I think C.

kron0s · Answer

(1) Two opposite sides of ABCD are equal in length.
(2) Two opposite internal angles of ABCD are right angles.

1. Let's assume AB=CD. This does not help us in determining the lengths of the other two sides or the angles between sides. ABCD could be a rectangle or a rhombus. Not sufficient.

2. Angle ABC= Angle BCD. This makes it a square or a rectangle. Not sufficient.

E

TarunKumar1234 · Answer

KalaAzar ! Square is type of rectangle. I feel, you can recheck your answer.

kron0s · Answer

I stand corrected. A Square can be considered as a type of a rectangle. I was trying to find similar questions online and came across the same one posted less than a month ago. You seem to have  answered the question  as well! Although the OA mentions E there, my reasoning seems to be off.

GCMEMBER · Answer

Is quadrilateral ABCD a rectangle?

(1) Two opposite sides of ABCD are equal in length.
ABCD can be a rectangle or a rhombus. 
Not sufficient.

(2) Two opposite internal angles of ABCD are right angles.
ABCD can be a rectangle or a Kite. 
Not sufficient.

(1) + (2)
Two opposite sides are equal.
And two opposite angles are 90 degrees.
ABCD is a rectangle. 
Sufficient

Option C

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amr0910 · Answer

I have a doubt.
By (2), two opposite internal angles are ABCD are right angles. By properties of quadrilateral, Sum of any two adjacent angles is 180. Therefore all angles are of 90 degrees, which is a property of rectangle. Square is a special case of Rectangle, and there is no information given about relation between adjacent sides. So shouldn't the answer be B?

CEdward · Answer

Where are the right angles located on the kite? Is it the "horizontal" angles or the two vertical angles?

Secondly, when you combine the statements, doesn't the kite still have two pairs of equal sides as well?

CrackverbalGMAT · Answer

Solution:

The question tests on the basic properties of quadrilaterals. Its an extremely important area and must be covered well.

St(1):-Two opposite sides of ABCD are equal in length.

No information is provided on the other sides. The figure can be a parallelogram too. (Insufficient)

Eliminate A,D

St(2):-Two opposite internal angles of ABCD are right angles

No information about the other angles

The other two angles can be 90 and 90 degrees or 130 and 50 and can both add up to 180.(So,  Insufficient)

Eliminate B

Combining 1 & 2,

We still do not know the other pair of angles

We can have a rectangle(a yes to the Question) or

We can have two right angle triangles joined at the common hypotenuse with different bases and =>We get an answer of "no" to the question.  (Insufficient)   (option e).
 
  Devmitra Sen
GMAT SME

RamseyGooner · Answer

Answer is C IMO

1) Opposite sides are equal.

Okay, very well. But what about the angles? So, this could be ||gram or rect, wdk.

Eliminate AD

2) Two opposite internal angles of ABCD are right angles.

What about the other two internal angles, wk that there sum is 180, so they can be 90 -90 (in case of which the answer could still have 2 alternatives, sq and rect) or lets say maybe 120 - 60. So, eliminate B.

Combine both,

Opposite sides are equal length. two of opposite angles are 90, therefore two of the remaining is supposed to be of same measure,i.e., 90.

Looks like we have a rectangle here.

Select C.

Hope this helps!

rye · Answer

Answer is C IMO

1) Opposite sides are equal.

Okay, very well. But what about the angles? So, this could be ||gram or rect, wdk.

Eliminate AD

/quote]

The question says in STatement 1 that "Two opposite sides are equal and "NOT ALL" opposite sides are equal". Thus, in the figure, only 2 opposite sides are equal. How did you deduce that 2 opposite sides mean ALL opposite sides are equal?

loki14 · Answer

HI , Can you please re-check,
I think we cannot create a quadrilateral with two right angled triangles joined at common hypotenuse by varying only the base..!
answer must be C

Hariharan1 · Answer

Hi
Can you please draw and show. Explanation not understood 
Thanks

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Is quadrilateral ABCD a rectangle? (1) Two opposite sides of ABCD are

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Is quadrilateral ABCD a rectangle? (1) Two opposite sides of ABCD are

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