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OlegC
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ABCD is a quadrilateral. A*, B*, C*, D* are midpoints of its 10 Aug 2004, 05:49
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ABCD is a quadrilateral. A*, B*, C*, D* are midpoints of its sides as shown in the picture. Is ABCD a rectangle?

(1) A*B*=B*C*=C*D*=A*D*
(2) AC is perpendicular to BD



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ABCD is a quadrilateral. A*, B*, C*, D* are midpoints of its 10 Aug 2004, 07:17
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(1)It can happen in rectangle or square. However, a square is also a rectangle. Thus, sufficient.

(2)It can happen in square or rhombus. Thus insufficient.

So A is the answer.

OlegC
ABCD is a quadrilateral. A*, B*, C*, D* are midpoints of its sides as shown in the picture. Is ABCD a rectangle?

(1) A*B*=B*C*=C*D*=A*D*
(2) AC is perpendicular to BD
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ABCD is a quadrilateral. A*, B*, C*, D* are midpoints of its 10 Aug 2004, 07:59
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Mallelac, from ur interpretation of statement 1, how do u establish the angles are right angles??
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ABCD is a quadrilateral. A*, B*, C*, D* are midpoints of its 10 Aug 2004, 13:20
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Statement 1 could also mean a Rhombus.
So i think the answer is C.
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ABCD is a quadrilateral. A*, B*, C*, D* are midpoints of its 10 Aug 2004, 21:58
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From my understanding of the geometry, only when the angles are right angles, the lines joining mid-points will be equal in length.

In a Rhombus, it does not happen so. You can visualize it very easily by drawing a Rhombus with 120 and 60 degrees.

cbrf3
Mallelac, from ur interpretation of statement 1, how do u establish the angles are right angles??
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ABCD is a quadrilateral. A*, B*, C*, D* are midpoints of its 10 Aug 2004, 23:04
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stem 1) Insufficient
stem 2) Insufficient. Can be a kite (one other type of a quadrilateral whose diaglonals can be perpendicular)

Combining both, we have the image below(rough sketch). I think we can csll it a turned square(like a diamond)...all sides equal and angels are 90 degree each. So the answer is C.

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Kite.JPG
Kite.JPG [ 9.9 KiB | Viewed 1855 times ]

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ABCD is a quadrilateral. A*, B*, C*, D* are midpoints of its 10 Aug 2004, 23:38
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this is good stuff. :-D

Olegc, you da man.
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ABCD is a quadrilateral. A*, B*, C*, D* are midpoints of its 11 Aug 2004, 01:08
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The answer is E

- obviously any square is an example of a rectangle in which both (1) and (2) are true
- the figure below is an example of a non-rectangle where (1) and (2) are also true
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ABCD is a quadrilateral. A*, B*, C*, D* are midpoints of its 11 Aug 2004, 01:16
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Bingo!!
Very tough to visualize in the 2 minutes. Good stuff.

OlegC
The answer is E

- obviously any square is an example of a rectangle in which both (1) and (2) are true
- the figure below is an example of a non-rectangle where (1) and (2) are also true
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ABCD is a quadrilateral. A*, B*, C*, D* are midpoints of its 13 Aug 2004, 06:42
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Oleg,
There seems some issue with the answer choice E. I selected C and I am wrong...

Thinking about it (also having discussed with a few friends), the answer should be B.

let me explain....

In a rectangle the diagonals are not Perpendicular. So, B is enough to say that ABCD is NOT a rectangle. This is a yes or no question. We have a firm No with B. Hence B. Think about it guys and let me know whats wrong with the argument. It can be a square or rhombus (both are NOT rectangles).
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ABCD is a quadrilateral. A*, B*, C*, D* are midpoints of its 16 Aug 2004, 00:31
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square is a rectangle by definition



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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