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# Is quadrilateral ABCD a rectangle? (1) Angle ABC and BCD are

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VP
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Is quadrilateral ABCD a rectangle? (1) Angle ABC and BCD are [#permalink]

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06 Sep 2007, 20:26
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(1) Angle ABC and BCD are right angles

(2) The diagonals of the quadrilateral are equal
Director
Joined: 03 May 2007
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06 Sep 2007, 21:43
bkk145 wrote:

(1) Angle ABC and BCD are right angles
(2) The diagonals of the quadrilateral are equal

C. I do not see any big complexity but certainly B is a trap.
Senior Manager
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06 Sep 2007, 22:00
What about square, can it be accepted as rectangle?

if yes than C
If no than E

Explantion needed:[/list]
GMAT Club Legend
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06 Sep 2007, 22:29
St1:
ABCD could be a trapezium.. insufficient.

St2:
Could be a square.

Using st1 and st2:
Could be a square or rectangle.

Ans E
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06 Sep 2007, 23:32
Ferihere wrote:
What about square, can it be accepted as rectangle?

if yes than C
If no than E

Explantion needed:[/list]

I encountered a similar question and was wondering about the same thing!! Any quant experts?????
GMAT Club Legend
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07 Sep 2007, 00:05
beckee529 wrote:
Ferihere wrote:
What about square, can it be accepted as rectangle?

if yes than C
If no than E

Explantion needed:[/list]

I encountered a similar question and was wondering about the same thing!! Any quant experts?????

No, a square is a square and a rectangle is a rectangle. Both are special forms of parallelograms with their own individual properties. For instance, the diagonals of a square intersect at right angles, but the diagonals of a rectangle don't.
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07 Sep 2007, 05:20
ywilfred wrote:
beckee529 wrote:
Ferihere wrote:
What about square, can it be accepted as rectangle?

if yes than C
If no than E

Explantion needed:[/list]

I encountered a similar question and was wondering about the same thing!! Any quant experts?????

No, a square is a square and a rectangle is a rectangle. Both are special forms of parallelograms with their own individual properties. For instance, the diagonals of a square intersect at right angles, but the diagonals of a rectangle don't.

ywilfred, sorry but I must disagree.

A square is at the same time:
> a rectangle
> a paralellogram

A square is a special rectangle with a right angle at the intersection of its diagonals ... or... with same length of edges

All properties from a rectangle are verified by a square, making it a rectangle... Indeed, we could represent the figures groups and sub-groups such as my attached picture

Some more references: http://www.mathopenref.com/square.html
Quote:
A square can be thought of as a special case of other quadrilaterals, for example

* a rectangle but with opposite sides equal
* a parallelogram but with opposite sides equal and the angles all 90°
* a rhombus but with angles all 90°

Attachments

Square.gif [ 5.87 KiB | Viewed 960 times ]

VP
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07 Sep 2007, 06:29
Thanks team.
I am sorry, but I don't know the OA for this one. I am debating with another person about this square/rectangle thing. I say C, but he say E. I just want to know which is correct...
SVP
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07 Sep 2007, 06:55
A similar debate with a question from MGMAT... the OA is provided

http://www.gmatclub.com/forum/viewtopic.php?t=39781
Senior Manager
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07 Sep 2007, 07:12
if a square can be accepted as rectangle than C

Ans: C

Thanks for Explanation
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07 Sep 2007, 07:26
bkk145 wrote:

(1) Angle ABC and BCD are right angles

(2) The diagonals of the quadrilateral are equal

Another C,

'a rectangle is defined as a quadrilateral where all four of its angles are right angles'

1 insuff- could be trapezoid
2 insuff- could be trapezoid with two equal sides

both suff, C, no way we can construct figure with two right angles and two diff diagonals.
Attachments

trpzd3.gif [ 2.14 KiB | Viewed 930 times ]

trpzd5.gif [ 2.22 KiB | Viewed 931 times ]

Re: Geometry DS   [#permalink] 07 Sep 2007, 07:26
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