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Is quadrilateral ABCD a square?

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Is quadrilateral ABCD a square?  [#permalink]

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New post 05 Aug 2014, 09:38
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Is quadrilateral ABCD a square?

(1) AB=BC
(2) ABCD is a rectangle.
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Re: Is quadrilateral ABCD a square?  [#permalink]

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New post 05 Aug 2014, 09:46
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goodyear2013 wrote:
Is quadrilateral ABCD a square?

(1) AB=BC
(2) ABCD is a rectangle.


From first we have ABCD is a square or Rhombus

From St 2, we have that Angles are at 90 deg

Combining we have AB=BC=CD=AD and all angles 90 deg.

Ans is C
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Re: Is quadrilateral ABCD a square?  [#permalink]

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New post 05 Aug 2014, 22:42
WoundedTiger wrote:
goodyear2013 wrote:
Is quadrilateral ABCD a square?

(1) AB=BC
(2) ABCD is a rectangle.


From first we have ABCD is a square or Rhombus

From St 2, we have that Angles are at 90 deg

Combining we have AB=BC=CD=AD and all angles 90 deg.

Ans is C


Yeah, (1) or (2) is insufficient
(1) and (2) is definitely a square !!! :-D
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Re: Is quadrilateral ABCD a square?  [#permalink]

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New post 28 Jan 2018, 22:14
1
WoundedTiger wrote:
goodyear2013 wrote:
Is quadrilateral ABCD a square?

(1) AB=BC
(2) ABCD is a rectangle.


From first we have ABCD is a square or Rhombus

From St 2, we have that Angles are at 90 deg

Combining we have AB=BC=CD=AD and all angles 90 deg.

Ans is C


hi

according to the statement 1, the quadrilateral does not have to be a rhombus also, because CD can be any straight line bigger than AB, and angle ADC can be an acute angle

taking 2 statements together we can see that the quadrilateral can only have 4 right angles, and so, CD cannot be larger than AB, and AB = BC

thus C is the answer

thanks, and cheers with kudos
:cool:
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Re: Is quadrilateral ABCD a square?  [#permalink]

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New post 29 Jan 2018, 18:17
Could anyone please explain why statement 2 is insufficient? Isn't there a property that says A rectangle can be a square as well?
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Re: Is quadrilateral ABCD a square?  [#permalink]

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New post 29 Jan 2018, 19:58
csaluja wrote:
Could anyone please explain why statement 2 is insufficient? Isn't there a property that says A rectangle can be a square as well?


A rectangle could be a square but it's not always a square. So, all squares are rectangles but not all rectangles are squares.

Check Properties of Polygons Questions from our Special Questions Directory.
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Is quadrilateral ABCD a square?  [#permalink]

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New post 30 Jan 2018, 04:21
csaluja wrote:
Could anyone please explain why statement 2 is insufficient? Isn't there a property that says A rectangle can be a square as well?



hi

you can see Bunuel the great has already replied to your confusion, however, for some elementary clarification, remember that

rectangle means, 4 right angles
square means, 4 right angles + all sides are equal

now, hope this is clear that all squares possess all the characteristics of rectangles, but
rectangles do not possess all the characteristics of squares

thanks, and cheers with kudos if this is clear to you!
:cool:
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Re: Is quadrilateral ABCD a square?  [#permalink]

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New post 22 Nov 2018, 17:47
goodyear2013 wrote:
Is quadrilateral ABCD a square?

(1) AB=BC
(2) ABCD is a rectangle.

\(ABCD\,\,\mathop = \limits^? \,\,{\text{square}}\)


\(\left( 1 \right)\,\,AB = BC\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{trivial}}\,\,{\text{geometric}}\,\,{\text{bifurcation}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{INSUFF}}.\)


\(\left( 2 \right)\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,{\text{ABCD}}\,\,{\text{rectangle}}\,\,{\text{non - square}} \hfill \\
\,{\text{Take}}\,\,{\text{ABCD}}\,\,\left( {{\text{rectangle}}\,\,{\text{and}}} \right)\,\,{\text{square}} \hfill \\
\end{gathered} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{INSUFF}}.\)


\(\left( {1 + 2} \right)\,\,\,\left\{ {\,\left. \begin{gathered}
\,{\text{rectangle}}\,\,\,\, \Rightarrow \,\,\,\,{\text{parallelogram}} \hfill \\
\,\,\left[ {AB = BC} \right]\,\, \cap \,\,{\text{parallelogram}}\,\,\,\, \Rightarrow \,\,\,\,{\text{rhombus}} \hfill \\
\end{gathered} \right\}} \right.\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,{\text{SUFF}}{\text{.}}\)

\(\left( * \right)\,\,\,\left\{ \begin{gathered}
\,{\text{rectangle}} \hfill \\
\,{\text{rhombus}} \hfill \\
\end{gathered} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{square}}\)


This solution follows the notations and rationale (quadrilaterals properties) taught in the GMATH method.

Regards,
Fabio.
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Re: Is quadrilateral ABCD a square? &nbs [#permalink] 22 Nov 2018, 17:47
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