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enigma123
Attachment:
ABCD.png
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD

In this question - How come the answer is C?

In Square the diagonals bisect each other at 90 degrees and are equal. How do we know that diagonals are bisecting each other at 90 degrees?


square has equal sides and equal diagonals.
rhombus has equal sides but not equal diagonals.
so both together are sufficient...... Answer (C)

About the 2nd question, let p the point of intersection ofthe two diagonal AC and BD.
now angle PAB = angle PBA [because PA=PB]
so angle APB has to be 90 or it will not be possible for the total angle surrounding the point P to be 360.
so diagonals have to bisect at 90 degress
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Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD


Hi,
1) statement tells us all sides are equal. it could be a rhombus , a square etc.... insuff
2) stat 2 tells us that the diagonals are equal.. it could be a rectangle , a square or any other quad.. insuff

combined we know it can only be a square... suff
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Hi!

We could also say from statement 1 that it could be any irregular quadrilateral (apart from being either a rhombus/sq). Again from statement 2 it can be concluded that the figure could be any irregular quad too. combining both cant it be concluded that the figure could be an irregular quadrilateral too?
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enigma123
Attachment:
ABCD.png
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD

In this question - How come the answer is C?

In Square the diagonals bisect each other at 90 degrees and are equal. How do we know that diagonals are bisecting each other at 90 degrees?

Solution:

Statement 1: It can be either a square or rhombus. Insufficient.
Statement 2: It can be either a square or a parallelogram or a rectangle.

Combining St 1 and St 2, It has to be a square.

Therefore the answer is Option C.
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I did this question in the following method. Correct me if i am wrong . From the statement 1 the quadrilateral can be a Rhombus or a square. Hence not sufficient. Now from statement 2 the quadrilateral is a rhombus or a square or a rectangle.
1 and 2 together C
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I did this question in the following method. Correct me if i am wrong . From the statement 1 the quadrilateral can be a Rhombus or a square. Hence not sufficient. Now from statement 2 the quadrilateral is a rhombusor a square or a rectangle.
1 and 2 together C

A rhombus with equal diagonal is a square.
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Statement 2: It can be either a square or a rectangle or any equidiagonal quadrilateral
Quadrilaterals with equal diagonal are called equidiagonal quadrilateral.
Attachment:
Equidiagonal Quandrilateral.jpg
Equidiagonal Quandrilateral.jpg [ 36.68 KiB | Viewed 12737 times ]


harikrish
enigma123
Attachment:
The attachment ABCD.png is no longer available
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD

In this question - How come the answer is C?

In Square the diagonals bisect each other at 90 degrees and are equal. How do we know that diagonals are bisecting each other at 90 degrees?

Solution:

Statement 1: It can be either a square or rhombus. Insufficient.
Statement 2: It can be either a square or a parallelogram or a rectangle or any equidiagonal quadrilateral.

Combining St 1 and St 2, It has to be a square.

Therefore the answer is Option C.
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