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# Is quadrilateral Q a square?

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Manager
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28 Nov 2007, 15:19
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(1) The sides of Q have the same length.
(2) The diagonals of Q have the same length
[Reveal] Spoiler: OA
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28 Nov 2007, 15:40
Expert's post
С. only both can let us a square.
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28 Nov 2007, 16:05
Expert's post
yogachgolf wrote:
why 'a' is insuff?

you can imagine four sticks with same length that are pinned by hinges. you can easily transform the square to a different rhombuses and even to a line.
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28 Nov 2007, 16:24
yogachgolf wrote:
(1) The sides of Q have the same length.
(2) The diagonals of Q have the same length

C

Here il post u a drawing.
Attachments

DS Geometry.doc [232 KiB]

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05 Aug 2010, 06:24
Statement 1 is not sufficient since a rhombus has 4 equal sides as well.

Statement 2 is not sufficient since a rectangle has equal diagonals.

Statements 1 and 2 are sufficient.
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25 Oct 2013, 06:35
shubhampandey wrote:
yogachgolf wrote:
walker wrote:
С. only both can let us a square.

why 'a' is insuff?

Because it can be a parellogram or rhombus..

In a parallelogram, not all the sides have the same length from what I understand.
Or am I missing something?
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25 Oct 2013, 08:28
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jlgdr wrote:
shubhampandey wrote:
yogachgolf wrote:

(1) The sides of Q have the same length.
(2) The diagonals of Q have the same length

In a parallelogram, not all the sides have the same length from what I understand.
Or am I missing something?

Parallelogram CAN have all 4 sides of equal length.

Parallelogram A quadrilateral with two pairs of parallel sides.

Properties and Tips
• Opposite sides of a parallelogram are equal in length.
• Opposite angles of a parallelogram are equal in measure.

• Opposite sides of a parallelogram will never intersect.
• The diagonals of a parallelogram bisect each other.
• Consecutive angles are supplementary, add to 180°.
The area, $$A$$, of a parallelogram is $$A = bh$$, where $$b$$ is the base of the parallelogram and $$h$$ is its height.
• The area of a parallelogram is twice the area of a triangle created by one of its diagonals.

A parallelogram is a quadrilateral with opposite sides parallel and congruent. It is the "parent" of some other quadrilaterals, which are obtained by adding restrictions of various kinds:
• A rectangle is a parallelogram but with all angles fixed at 90°
• A rhombus is a parallelogram but with all sides equal in length
• A square is a parallelogram but with all sides equal in length and all angles fixed at 90°

For other properties check polygons chapter of Math Book: math-polygons-87336.html
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15 Apr 2014, 01:10
HI Bunnel,

As you have mentioned that Parallelogram can have four sides equal then definitely its diagonals are also equal and it will become square. why A is not right?
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15 Apr 2014, 01:19
Expert's post
HI Bunnel,

As you have mentioned that Parallelogram can have four sides equal then definitely its diagonals are also equal and it will become square. why A is not right?

If a parallelogram has equal sides it is a rhombus but rhombus is not necessary to have equal diagonals, or in other words not all rhombuses are squares:

Hope it's clear.
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05 Jun 2014, 03:43
A is insufficient cause rhombus is a quadrilateral with four sides & diagonals of dfferent lengths
B is insufficient cause a uniform Trapezoid has both the diagonals equal..

C is sufficient as trapezoid and rhombus are both eliminated.Hence a square
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05 Jun 2014, 03:45
GMATBLACKBELT wrote:
yogachgolf wrote:
(1) The sides of Q have the same length.
(2) The diagonals of Q have the same length

C

Here il post u a drawing.

This is an incorrect explanation cause a hexagon is not a quadrilateral and instead a uniform trapezium or a rectangle is a better alternative
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Last edited by JusTLucK04 on 05 Jun 2014, 05:20, edited 1 time in total.
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05 Jun 2014, 03:50
yogachgolf wrote:

(1) The sides of Q have the same length.
(2) The diagonals of Q have the same length

Statement I is insufficient:

Rhombus have same lengths and so does a square.

Statement II is insufficient:

Sides may or may not be same.

Combining is sufficient:

If sides are same and diagonals are same which means all the sides must intersect at ninety degrees hence answer is c.
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Re: Is quadrilateral Q a square? (1) The sides of Q have the [#permalink]

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28 Sep 2015, 01:57
C is the answer as it can be solved by using both the statements.
Re: Is quadrilateral Q a square? (1) The sides of Q have the   [#permalink] 28 Sep 2015, 01:57
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