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Is quadrilateral ABCD a rectangle?

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Is quadrilateral ABCD a rectangle?  [#permalink]

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New post Updated on: 06 Jun 2015, 10:50
1
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A
B
C
D
E

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Is quadrilateral ABCD a rectangle?

(1) All four sides of ABCD are equal.

(2) All four internal angles of ABCD are equal.

SOLUTION:
The issue is finding whether ABCD is a rectangle. A rectangle is a quadrilateral with parallel sides and four right angles.

According to Stat. (1) ABCD can be a square, which a subcategory of rectangle, yielding an answer of "yes". However, ABCD can also be a rhombus, which does not have right angles, and then then answer is "no". No definite answer, so Stat.(1)->maybe->IS->BCE.

Stat. (2): the sum of the angles in a quadrilateral is 360 degrees. If all angles are equal, each of them measure 360 / 4 = 90°. Therefore, ABCD is a rectangle (it can also be a square, which is a subcategory of a rectangle), and the answer is a definite "yes".
Stat.(2)->'yes'->S->B.

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Originally posted by reto on 06 Jun 2015, 04:24.
Last edited by Bunuel on 06 Jun 2015, 10:50, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Is quadrilateral ABCD a rectangle?  [#permalink]

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New post 06 Jun 2015, 14:04
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It's very important to be crystal clear on your definitions of shapes. People often take shapes like squares and rectangles for granted, because they know well what they look like, but be solid with the definitions as well.

Is quadrilateral ABCD a rectangle?
A rectangle is a quadrilateral with 2 pairs of equal sides and 4 90 degree angles. Squares are a special type of rectangle.

(1) All four sides of ABCD are equal.
This could be a square (and thus a rectangle) because it meets the requirement of having 2 pairs of equal sides. However, it does not necessarily meet the requirement of having four angles of 90 degrees, and thus could possibly be a rhombus. Insufficient.

(2) All four internal angles of ABCD are equal.
Quadrilaterals have angles that add to 360 degrees. You know what the angle measurements of a shape should add to by adding the sides of the shape, subtracting 2, and then multiplying by 180. For example, triangle -> (3-2)*180 = 180. quadrilateral -> (4-2)*180 = 360. pentagon -> (5-2)*180 = 540. etc. Because these angles are all 90 degrees, the shape is definitely a form of rectangle. Thus we have a definitely sufficient and a correct answer.

Answer choice B. I hope this helps!
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Re: Is quadrilateral ABCD a rectangle?  [#permalink]

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New post 04 Aug 2015, 12:27
VeritasPrepBrandon wrote:
It's very important to be crystal clear on your definitions of shapes. People often take shapes like squares and rectangles for granted, because they know well what they look like, but be solid with the definitions as well.

Is quadrilateral ABCD a rectangle?
A rectangle is a quadrilateral with 2 pairs of equal sides and 4 90 degree angles. Squares are a special type of rectangle.

(1) All four sides of ABCD are equal.
This could be a square (and thus a rectangle) because it meets the requirement of having 2 pairs of equal sides. However, it does not necessarily meet the requirement of having four angles of 90 degrees, and thus could possibly be a rhombus. Insufficient.

(2) All four internal angles of ABCD are equal.
Quadrilaterals have angles that add to 360 degrees. You know what the angle measurements of a shape should add to by adding the sides of the shape, subtracting 2, and then multiplying by 180. For example, triangle -> (3-2)*180 = 180. quadrilateral -> (4-2)*180 = 360. pentagon -> (5-2)*180 = 540. etc. Because these angles are all 90 degrees, the shape is definitely a form of rectangle. Thus we have a definitely sufficient and a correct answer.




Answer choice B. I hope this helps!





Hi Brandon,

Just a small doubt here.
As mentioned in statement B that all internal angles are equal, so that gives us clue that all the angles are equal to 90.
But this can be true for square also , so how can we determine its rectangle.
It can be square also.

Kindly let me know what I am missing here
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Re: Is quadrilateral ABCD a rectangle?  [#permalink]

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New post 04 Aug 2015, 12:32
kanigmat011 wrote:


Hi Brandon,

Just a small doubt here.
As mentioned in statement B that all internal angles are equal, so that gives us clue that all the angles are equal to 90.
But this can be true for square also , so how can we determine its rectangle.
It can be square also.

Kindly let me know what I am missing here


Rectangle is the BIGGER category while square is a special type of rectangle that has all angles equal to 90, all sides equal and diagonals being perpendicular bisectors of each other. Thus any square will always be a rectangle but the vice versa may or may not be true (as for a square you also need to have all angles = 90).
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Is quadrilateral ABCD a rectangle?  [#permalink]

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New post 04 Aug 2015, 12:32
kanigmat011 wrote:
VeritasPrepBrandon wrote:
It's very important to be crystal clear on your definitions of shapes. People often take shapes like squares and rectangles for granted, because they know well what they look like, but be solid with the definitions as well.

Is quadrilateral ABCD a rectangle?
A rectangle is a quadrilateral with 2 pairs of equal sides and 4 90 degree angles. Squares are a special type of rectangle.

(1) All four sides of ABCD are equal.
This could be a square (and thus a rectangle) because it meets the requirement of having 2 pairs of equal sides. However, it does not necessarily meet the requirement of having four angles of 90 degrees, and thus could possibly be a rhombus. Insufficient.

(2) All four internal angles of ABCD are equal.
Quadrilaterals have angles that add to 360 degrees. You know what the angle measurements of a shape should add to by adding the sides of the shape, subtracting 2, and then multiplying by 180. For example, triangle -> (3-2)*180 = 180. quadrilateral -> (4-2)*180 = 360. pentagon -> (5-2)*180 = 540. etc. Because these angles are all 90 degrees, the shape is definitely a form of rectangle. Thus we have a definitely sufficient and a correct answer.




Answer choice B. I hope this helps!





Hi Brandon,

Just a small doubt here.
As mentioned in statement B that all internal angles are equal, so that gives us clue that all the angles are equal to 90.
But this can be true for square also , so how can we determine its rectangle.
It can be square also.

Kindly let me know what I am missing here



Hello kanigmat011

Square is a type of rectangle.

So square is always a rectangle
but rectangle is not always a square
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Re: Is quadrilateral ABCD a rectangle?  [#permalink]

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New post 04 Aug 2015, 13:18
Harley1980 wrote:
kanigmat011 wrote:
VeritasPrepBrandon wrote:
It's very important to be crystal clear on your definitions of shapes. People often take shapes like squares and rectangles for granted, because they know well what they look like, but be solid with the definitions as well.

Is quadrilateral ABCD a rectangle?
A rectangle is a quadrilateral with 2 pairs of equal sides and 4 90 degree angles. Squares are a special type of rectangle.

(1) All four sides of ABCD are equal.
This could be a square (and thus a rectangle) because it meets the requirement of having 2 pairs of equal sides. However, it does not necessarily meet the requirement of having four angles of 90 degrees, and thus could possibly be a rhombus. Insufficient.

(2) All four internal angles of ABCD are equal.
Quadrilaterals have angles that add to 360 degrees. You know what the angle measurements of a shape should add to by adding the sides of the shape, subtracting 2, and then multiplying by 180. For example, triangle -> (3-2)*180 = 180. quadrilateral -> (4-2)*180 = 360. pentagon -> (5-2)*180 = 540. etc. Because these angles are all 90 degrees, the shape is definitely a form of rectangle. Thus we have a definitely sufficient and a correct answer.




Answer choice B. I hope this helps!





Hi Brandon,

Just a small doubt here.
As mentioned in statement B that all internal angles are equal, so that gives us clue that all the angles are equal to 90.
But this can be true for square also , so how can we determine its rectangle.
It can be square also.

Kindly let me know what I am missing here



Hello kanigmat011

Square is a type of rectangle.

So square is always a rectangle
but rectangle is not always a square


Thanks Harvey

It just never popped my head.
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Re: Is quadrilateral ABCD a rectangle?  [#permalink]

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New post 04 Aug 2015, 13:23
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Re: Is quadrilateral ABCD a rectangle?  [#permalink]

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New post 04 Aug 2015, 13:34
Engr2012 wrote:
kanigmat011 wrote:


Hi Brandon,

Just a small doubt here.
As mentioned in statement B that all internal angles are equal, so that gives us clue that all the angles are equal to 90.
But this can be true for square also , so how can we determine its rectangle.
It can be square also.

Kindly let me know what I am missing here


Rectangle is the BIGGER category while square is a special type of rectangle that has all angles equal to 90, all sides equal and diagonals being perpendicular bisectors of each other. Thus any square will always be a rectangle but the vice versa may or may not be true (as for a square you also need to have all angles = 90).



Thanks Engr2012
Now its clear!
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Re: Is quadrilateral ABCD a rectangle?  [#permalink]

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New post 08 May 2017, 06:25
VeritasPrepBrandon wrote:
It's very important to be crystal clear on your definitions of shapes. People often take shapes like squares and rectangles for granted, because they know well what they look like, but be solid with the definitions as well.

Is quadrilateral ABCD a rectangle?
A rectangle is a quadrilateral with 2 pairs of equal sides and 4 90 degree angles. Squares are a special type of rectangle.

(1) All four sides of ABCD are equal.
This could be a square (and thus a rectangle) because it meets the requirement of having 2 pairs of equal sides. However, it does not necessarily meet the requirement of having four angles of 90 degrees, and thus could possibly be a rhombus. Insufficient.

(2) All four internal angles of ABCD are equal.
Quadrilaterals have angles that add to 360 degrees. You know what the angle measurements of a shape should add to by adding the sides of the shape, subtracting 2, and then multiplying by 180. For example, triangle -> (3-2)*180 = 180. quadrilateral -> (4-2)*180 = 360. pentagon -> (5-2)*180 = 540. etc. Because these angles are all 90 degrees, the shape is definitely a form of rectangle. Thus we have a definitely sufficient and a correct answer.

Answer choice B. I hope this helps!

One doubt: Is it true that in DS and PS question, we have to consider every Square as a rectangle by default?


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Re: Is quadrilateral ABCD a rectangle?  [#permalink]

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New post 08 May 2017, 08:53
goalMBA1990 wrote:
VeritasPrepBrandon wrote:
It's very important to be crystal clear on your definitions of shapes. People often take shapes like squares and rectangles for granted, because they know well what they look like, but be solid with the definitions as well.

Is quadrilateral ABCD a rectangle?
A rectangle is a quadrilateral with 2 pairs of equal sides and 4 90 degree angles. Squares are a special type of rectangle.

(1) All four sides of ABCD are equal.
This could be a square (and thus a rectangle) because it meets the requirement of having 2 pairs of equal sides. However, it does not necessarily meet the requirement of having four angles of 90 degrees, and thus could possibly be a rhombus. Insufficient.

(2) All four internal angles of ABCD are equal.
Quadrilaterals have angles that add to 360 degrees. You know what the angle measurements of a shape should add to by adding the sides of the shape, subtracting 2, and then multiplying by 180. For example, triangle -> (3-2)*180 = 180. quadrilateral -> (4-2)*180 = 360. pentagon -> (5-2)*180 = 540. etc. Because these angles are all 90 degrees, the shape is definitely a form of rectangle. Thus we have a definitely sufficient and a correct answer.

Answer choice B. I hope this helps!

One doubt: Is it true that in DS and PS question, we have to consider every Square as a rectangle by default?


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Yes, but it has nothing to do with DS or PS specifically. Mathematically every square is a rectangle.
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Re: Is quadrilateral ABCD a rectangle?  [#permalink]

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New post 12 Jan 2018, 01:27
kanigmat011 wrote:
VeritasPrepBrandon wrote:
It's very important to be crystal clear on your definitions of shapes. People often take shapes like squares and rectangles for granted, because they know well what they look like, but be solid with the definitions as well.

Is quadrilateral ABCD a rectangle?
A rectangle is a quadrilateral with 2 pairs of equal sides and 4 90 degree angles. Squares are a special type of rectangle.

(1) All four sides of ABCD are equal.
This could be a square (and thus a rectangle) because it meets the requirement of having 2 pairs of equal sides. However, it does not necessarily meet the requirement of having four angles of 90 degrees, and thus could possibly be a rhombus. Insufficient.

(2) All four internal angles of ABCD are equal.
Quadrilaterals have angles that add to 360 degrees. You know what the angle measurements of a shape should add to by adding the sides of the shape, subtracting 2, and then multiplying by 180. For example, triangle -> (3-2)*180 = 180. quadrilateral -> (4-2)*180 = 360. pentagon -> (5-2)*180 = 540. etc. Because these angles are all 90 degrees, the shape is definitely a form of rectangle. Thus we have a definitely sufficient and a correct answer.




Answer choice B. I hope this helps!





Hi Brandon,

I'm still confused . Even if we know all angles are equal & 90 degree that gives us , no information about sides being equal to each other. Unless we combine both statement 1 & 2 .The option should have been C.

Please help in explaining how ans choice B alone is sufficient. Thanks in advance.
Re: Is quadrilateral ABCD a rectangle? &nbs [#permalink] 12 Jan 2018, 01:27
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