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# Is ABCD a rectangle? 1) AC(imagine: diagonal of a

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Is ABCD a rectangle? 1) AC(imagine: diagonal of a [#permalink]  08 Aug 2003, 10:55
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Is ABCD a rectangle?

1) AC(imagine: diagonal of a quadrilateral) bisect BD (imagine: another diagonal of a quadrilateral) bisect each other in point E
2) Angle ABC = 90 degrees
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[#permalink]  08 Aug 2003, 22:22
A only says the figure is a parallelogram --> opposite angles equal. B says one angle is 90. Together the two statements call for a rectangle. Right Stolyar ?
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Re: DS practice # 9 [#permalink]  09 Aug 2003, 04:47
Konstantin Lynov wrote:
Is ABCD a rectangle?

1) AC(imagine: diagonal of a quadrilateral) bisect BD (imagine: another diagonal of a quadrilateral) bisect each other in point E
2) Angle ABC = 90 degrees

My answer is E

(1) Tells us that the figure could be a rectangle or a square
(2) Tells us that, again, the figure could be a rectangle or a square

Combining, we still cannot be sure if its a rectangle or a square. Therefore, E
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[#permalink]  09 Aug 2003, 04:59
No Prashant bhai, (1) only tells you that the figure is a parallelogram. Yes it could also be a rhombus/Rectangle/Square.
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[#permalink]  09 Aug 2003, 05:01
anupag wrote:
No Prashant bhai, (1) only tells you that the figure is a parallelogram. Yes it could also be a rhombus/Rectangle/Square.

Agreed. But the answer remains the same. What do you say?
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[#permalink]  09 Aug 2003, 06:20
Is the statement "All squres are rectangle" true?
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[#permalink]  09 Aug 2003, 08:32
Is the statement "All squres are rectangle" true?

All squares are special cases of rhombuses and rectangles (and trapezoids), and all rhombuses and rectangles are special cases of paralleograms which are in turn special cases of trapezoids which are in turn special cases of quadrilaterals.
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Manager
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Re: DS practice # 9 [#permalink]  11 Aug 2003, 07:12
Konstantin Lynov wrote:
Is ABCD a rectangle?

1) AC(imagine: diagonal of a quadrilateral) bisect BD (imagine: another diagonal of a quadrilateral) bisect each other in point E
2) Angle ABC = 90 degrees

As I see opinions differ.
The key here lies in the word bisect, which is to divide in halfs.

From the first statement the figure could be a rombus and a rectangle. Insufficient.

From the second statement it could be anything with a 90 degree angle. Imagine an ugly figure with two relatively short sides and a 90 degree angle between them and with third and forth sides realy-realy long ones, ending up in the stratosphere. Insufficient.

Combining the statement is sufficient.
Re: DS practice # 9   [#permalink] 11 Aug 2003, 07:12
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# Is ABCD a rectangle? 1) AC(imagine: diagonal of a

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