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Is this figure a square? (There was a drawing of a square

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Manager
Joined: 21 Aug 2004
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Is this figure a square? (There was a drawing of a square [#permalink]  15 Sep 2004, 08:30
4. Is this figure a square? (There was a drawing of a square given with one angle shown as X degrees and the one opposite it on the same side shown as Y degrees)
1) All four sides are equal
2) X+Y=180 degrees
Manager
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E.

We are not given whether X and Y are equal. By the given information it could be either square or rhombus.
Director
Joined: 31 Aug 2004
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C

4 equal sides does not bring enough data, x+y either

2 stems together k
Director
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I agree with crackjgmat3 here. It can still be a rhombus. I will choose E too.
Manager
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if I understand the text right , a quadrilateral ABCD with <A=X , <C=Y

from the first data we can know that it is a rhombus

from second x+y = 180
we know also that the opposite angles of rhombus(parallelogram) are equal also
so x = y

solving we get x = y = 90 . so it becomes a square. Answer (c)

A figure is needed to guide in the solution.
Director
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E it is. To prove a square:
1. Four sides should be equal and the diagonals should be equal.
OR
2. Four sides should be equal and 2 adjacent angles should be 90.
Director
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Amer draw something interesting i did not write :

in a rhombus, 2 opposite angles are supposed to be equal aren't they ?
in this case x = y = 90

And a rhombus with a square angle is at least a rectangle and with 4 equal sides a square.
Director
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was a drawing of a square given with one angle shown as X degrees and the one opposite it on the same side shown as Y degrees

Amer, you might be mistaken to say <A + <C = 180, it should be <A+<B = 180

Twixt, Even if two sides of a rhombus are 90 degrees, it is not a square. You can draw a rhombus with 90, 60, 90, 130 degrees.
Manager
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A --------------------- B

D ---------------------C

let me give some of the properties of quadrilaterals that are used.

1. a rhombus is a parallelogram
2. opposite angles of a parallegram are equal ( A and C, B and D)
3. adjacent angles of a parallelogram ar supplementary (< A +< B=180, B and C , C and D, D and A )
4. from 2 and 3 we can deduce that a rhombus with one right angle is a square

Going back to the question.

It says the angle opposite to X on same side. This phrase is vague . If he means that <A and < B for example, he should have chosen the word adjacent or relied on a figure. If he means this then the answer would be E since the 2nd information (X+Y=180) is a known property of a rhombus and solution is E.

For your suggestion of a rhombus with 90,60,90,130. This figure is not a quadrilateral since sum of angles is 370. Furthermore as I earlier said a rhombus with one right angle is a square.

Hope this gives a clear understanding of my argument. I do believe that the problem with a figure would have cleared everything.
Director
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amernassar wrote:
Furthermore as I earlier said a rhombus with one right angle is a square.

My mistake. Agree that rhombus with atleast one 90 degrees is a square.
What I meant to say was, "A quadrilateral with sum of two opposite angles = 180 is not necessarilly a rectangle or square." The fact that the four sides are equal thows in a different light.
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90-90.JPG [ 2.4 KiB | Viewed 574 times ]

Manager
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yes it is my undertanding that if all sides are equal then it must be a paralellogram--correct?

if this is so, then two OPPOSITE angles would be equal and if their total is 180 then they must be 90 degrees making the object a square. is there some flaw in this logic????
Intern
Joined: 12 Sep 2004
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If all the sides are equal then the figure must be a sqare or a parallelogram.

Based on that the data provided is not enough. E is the correct answer.
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