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# Is quadrilateral ABCD a rectangle?

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Manager
Joined: 24 Jul 2009
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23 Jan 2010, 21:18
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39
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Difficulty:

55% (hard)

Question Stats:

49% (01:01) correct 51% (01:00) wrong based on 659 sessions

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(1) Line segments AC and BD bisect one another.
(2) Angle ABC is a right angle.

Rephrase: does ABCD have 1)opposite sides that are parallel and equal, 2) bisecting diagonals and 3) opposite and equal angles of 90; adjacent angles that sum to 180.

(1) Line segments AC and BD bisect one another.
Bisecting diagonals make quadrilateral ABCD a parallelogram but not necessarily a rectangle.

(2) Angle ABC is a right angle.
One right angle isn't enough to establish that quadrilateral ABCD is a rectangle.

Answer C: A paralleogram with one right angle has all right angles because opposite angles are equal. Therefore ABCD is a rectangle

Source: MGMAT question bank
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26 Feb 2010, 08:30
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Statement 1: Line segments AC and BD bisect one another. This is the case for rectangle, square and rhombus.
Not suff.
Stetement 2: Angle ABC is a right angle.
Any quadrilateral can have one right angle and other different angle. Not Suff.

Combining both statements could give us either rectangle or a square. Not suff.
##### General Discussion
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07 Aug 2010, 15:31
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Statement 1: Line segments AC and BD bisect one another. This is the case for rectangle, square and rhombus.
Not suff.
Stetement 2: Angle ABC is a right angle.
Any quadrilateral can have one right angle and other different angle. Not Suff.

Combining both statements could give us either rectangle or a square. Not suff.

But isn't square a specific case of rectangle. That way i would say answer is C
Intern
Joined: 30 Mar 2010
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21 Aug 2010, 07:57
OK! What if it is a right trapezoid? I mean it will have one (even two) right angles, the segments AC and BD will bisect one another and at the same time it will not be a rectagle. What in this case?
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22 Aug 2010, 11:46
@ mossovet814: If it is a trapezoid then the diagonals (AC and BD) won't bisect each other.

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22 Aug 2010, 13:27
pankajattri wrote:
@ mossovet814: If it is a trapezoid then the diagonals (AC and BD) won't bisect each other.

OK! This is a right trapezoid. Two angles are right and diagonals bisect one another. Still it is not a rectangle. I know the question is stupid... but I just want to find a flaw in my reasoning.
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trapezoid.jpg [ 10.88 KiB | Viewed 27046 times ]

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22 Aug 2010, 14:13
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Financier
Ok I must admit I am confused. Diagonals of a trapezoid bisect each other?
a). Diagonals of quadrangle allways bisect each other.
b). Trapezoid is a specific case of quadrangle .
I don't think that the diagonals of a trapezoid bisect each other.

Financier wrote:
pankajattri wrote:
@ mossovet814: If it is a trapezoid then the diagonals (AC and BD) won't bisect each other.

Dear Pankajattri,

First of all, I strongly suggest that you review the basics of Geometry so that you could recall that:
a). Diagonals of quadrangle allways bisect each other.
b). Trapezoid is a specific case of quadrangle .

Second, the Rules of GMATclub suppose that folks do not just utter statements without any foundation,
but rather unveil what rules they are based on. Above are the statements that prove that diagonals of Trapezoid intersect each other.

Third, the correct answer is E.
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22 Aug 2010, 18:04
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Dear Financier,

Even If I was wrong, which by the way I am not, I don't know why couldn't you find a more suitable way of posting your comment.

As for as the question is concerned; the diagonals of a PARALLELOGRAM bisect each other and not of each QUADRANGLE. All parallelograms are quadrangles but not vice versa.

I really hope that you know what does "bisection", "quadrangle" and "parallelogram" mean.

And next time please do not utter statements without any foundation.
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Joined: 18 Jun 2010
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22 Aug 2010, 23:22
Pankajattri,

I was wrong, excuse me and my tone. I'm soooo sorry. I messed up words "bisect" and "intersect". This happens when people study a lot. The correct answer is "C".
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31 Mar 2011, 19:36
Also, square is a type (subclass) of rectangle.

It's quite self-explanatory, for more information refer to Math Book in GMATClub.
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01 Apr 2011, 07:13
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@gmat1220

Here it is :

math-polygons-87336.html
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14 Nov 2012, 13:10
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Guys just wanted to add . as I had little confusion when I first saw this question --

From (1) ----> The diagonals bisect each other , ----> its a ||gm , for it to be a recrangle both diagonals should be equal.
From(2) ----> |_ ABC= 90 ----> clearly not sufficient.

When we combine both 1 & 2 ----> Its a ||gm with one angle 90. ----> that has to be a rectangle and both diagonals become automatically equivalent.
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31 Jul 2014, 02:20
1
I don't understand this.

Question: IS ABCD rectangle?

If we take "C", couldn't it still be a square?? Or is a square a "special rectangle with 4 equal sides"?

Thanks for you help.

Cheers
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31 Jul 2014, 07:51
unceldolan wrote:
I don't understand this.

Question: IS ABCD rectangle?

If we take "C", couldn't it still be a square?? Or is a square a "special rectangle with 4 equal sides"?

Thanks for you help.

Cheers

All squares are rectangles, so the answer would still be YES.
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12 Aug 2015, 04:07
319 wrote:
(1) Line segments AC and BD bisect one another.

(2) Angle ABC is a right angle.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Why is the answer C? and not E? It can be a square and not a rectangle.

I guess square is a special rectangle. I am not sure whether we can consider like this. Thoughts
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12 Aug 2015, 04:37
319 wrote:
(1) Line segments AC and BD bisect one another.

(2) Angle ABC is a right angle.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Why is the answer C? and not E? It can be a square and not a rectangle.

1. Please search for a question before you post.

2. Stick to formatting guidelines.

Topics merged.

As for your question, a square is a special type of rectangle that has all sides equal. Thus all squares are rectangles as well but not all rectangles are squares.
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Re: Is quadrilateral ABCD a rectangle? (1) Line segments AC and  [#permalink]

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26 Mar 2016, 09:51
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agautam7879 wrote:
(1) Line segments AC and BD bisect one another.

(2) Angle ABC is a right angle.

For me the answer should be E...because the ABCD could be a square as well...please comment

option B does not tell us whether all angles are 90. How option C is correct
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26 Mar 2016, 10:12
smartguy595 wrote:
agautam7879 wrote:
(1) Line segments AC and BD bisect one another.

(2) Angle ABC is a right angle.

For me the answer should be E...because the ABCD could be a square as well...please comment

option B does not tell us whether all angles are 90. How option C is correct

From (1) ABCD is a rectangle or a parallelogram. A parallelogram with a right angle is a rectangle.
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07 Jul 2017, 22:55
Can anyone articulate how we deduce from the fact that, if one angle of a parallelogram is 90 degrees and the opposite angle is equal, how do we come to the conclusion that the other pair of opposite angles are also equal to 90 degrees?
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08 Jul 2017, 04:29
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700byforce wrote:
Can anyone articulate how we deduce from the fact that, if one angle of a parallelogram is 90 degrees and the opposite angle is equal, how do we come to the conclusion that the other pair of opposite angles are also equal to 90 degrees?

Useful property: the adjacent angles of a parallelogram are supplementary (supplementary angles are two angles that add up to 180°). So, if angle B is 90°, then A and C must also be 90° to add up to 180.

Hope it helps.
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