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# If A, B and C are distinct points, do line segments AB and BC have the

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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]
3
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metallicafan wrote:
Bunuel wrote:
Straight E:

If ABCD is a square, then AB=BC but if ABCD is NOT a square, so if it's just a rectangle, then AB and BC won't have the same length. Not sufficient.

Bunuel, but the clue #1 says that ABCD is a rectangle. It is not necessary to evaluate whether it is a square or a rectangle.

I don't understand what you mean by the read part above.

As for the first statement: it says that ABCD is a rectangle, but since ALL squares are rectangles then ABCD could be a square or a rectangle which is not a square.
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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]
Bunuel wrote:
metallicafan wrote:
Bunuel wrote:
Straight E:

If ABCD is a square, then AB=BC but if ABCD is NOT a square, so if it's just a rectangle, then AB and BC won't have the same length. Not sufficient.

Bunuel, but the clue #1 says that ABCD is a rectangle. It is not necessary to evaluate whether it is a square or a rectangle.

I don't understand what you mean by the read part above.

As for the first statement: it says that ABCD is a rectangle, but since ALL squares are rectangles then ABCD could be a square or a rectangle which is not a square.

Ok, now I understand. I thought that, in the terminology, a rectangle could not be a "rectangle".
Thanks!
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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]
Bunuel, another question:

When the question says: Together with point D, A, B, and C form a rectangle.
Is there a specific order in which the points are set?
For example, if we start in the left lower vertex of the rectangle as Point A and then continue to the left upper vertex as point B, and so on....¿would it be the correct order?

In general, when the GMAT says, for example, "a triangle ABC....", is there a specific vertex in which we should start and a orientation that we have to follow?
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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]
metallicafan wrote:
Bunuel, another question:

When the question says: Together with point D, A, B, and C form a rectangle.
Is there a specific order in which the points are set?
For example, if we start in the left lower vertex of the rectangle as Point A and then continue to the left upper vertex as point B, and so on....¿would it be the correct order?

In general, when the GMAT says, for example, "a triangle ABC....", is there a specific vertex in which we should start and a orientation that we have to follow?

Generally when we are given "quadrilateral ABCD" or "triangle PQR", then it means that vertices are in that particular order only.
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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]
I got little confused.......it is said that together with D, A, B, and C form a rectangle.....doesn't that mean AB and BC are not equal??
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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]
4112019 wrote:
I got little confused.......it is said that together with D, A, B, and C form a rectangle.....doesn't that mean AB and BC are not equal??

All squares are rectangles, so if ABCD IS a square then AB=BC. Look at the figures below:
Attachment:

Square and Rectangle.png [ 3.33 KiB | Viewed 7086 times ]
The first figure is a rectangle which IS a square, so in this case AB=BC and the second figure is a rectangle which is NOT a square, so in this case AB#BC.

Hope it's clear.
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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]
Bunuel wrote:
4112019 wrote:
I got little confused.......it is said that together with D, A, B, and C form a rectangle.....doesn't that mean AB and BC are not equal??

All squares are rectangles, so if ABCD IS a square then AB=BC. Look at the figures below:
Attachment:
Square and Rectangle.png
The first figure is a rectangle which IS a square, so in this case AB=BC and the second figure is a rectangle which is NOT a square, so in this case AB#BC.

Hope it's clear.

Sorry Bunuel for picking on this..just want to be completely sure. So unless it's specified that the figure is a square (or it forms a square), we are to assume that a rectangle means both a square and non-square?
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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]
RMART wrote:
Bunuel wrote:
4112019 wrote:
I got little confused.......it is said that together with D, A, B, and C form a rectangle.....doesn't that mean AB and BC are not equal??

All squares are rectangles, so if ABCD IS a square then AB=BC. Look at the figures below:
Attachment:
Square and Rectangle.png
The first figure is a rectangle which IS a square, so in this case AB=BC and the second figure is a rectangle which is NOT a square, so in this case AB#BC.

Hope it's clear.

Sorry Bunuel for picking on this..just want to be completely sure. So unless it's specified that the figure is a square (or it forms a square), we are to assume that a rectangle means both a square and non-square?

If it's given that a figure is a rectangle, then it could be a square because all squares are rectangles (but not all rectangles are squares).
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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]
Bunuel wrote:
metallicafan wrote:
Bunuel, another question:

When the question says: Together with point D, A, B, and C form a rectangle.
Is there a specific order in which the points are set?
For example, if we start in the left lower vertex of the rectangle as Point A and then continue to the left upper vertex as point B, and so on....¿would it be the correct order?

In general, when the GMAT says, for example, "a triangle ABC....", is there a specific vertex in which we should start and a orientation that we have to follow?

Generally when we are given "quadrilateral ABCD" or "triangle PQR", then it means that vertices are in that particular order only.

But the real question is what is the order? Like for a triangle for example is P upper vertex then Q for the left vertex and R for the right vertex? And in a square do we go clockwise? Anticlockwise?

Thanks
Cheers
J
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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]
jlgdr wrote:
Bunuel wrote:
metallicafan wrote:
Bunuel, another question:

When the question says: Together with point D, A, B, and C form a rectangle.
Is there a specific order in which the points are set?
For example, if we start in the left lower vertex of the rectangle as Point A and then continue to the left upper vertex as point B, and so on....¿would it be the correct order?

In general, when the GMAT says, for example, "a triangle ABC....", is there a specific vertex in which we should start and a orientation that we have to follow?

Generally when we are given "quadrilateral ABCD" or "triangle PQR", then it means that vertices are in that particular order only.

But the real question is what is the order? Like for a triangle for example is P upper vertex then Q for the left vertex and R for the right vertex? And in a square do we go clockwise? Anticlockwise?

Thanks
Cheers
J

Square ABCD means that the order of the vertices is A, B, C, D. Usually it does not matter whether you go clockwise or anticlockwise.
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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]
metallicafan wrote:
If A, B, and C are distinct points, do line segments AB and BC have the same length?

(1) Together with point D, A, B, and C form a rectangle.
(2) AB is not equal to AC

Source: https://www.gmathacks.com

We need to know whether AB = BC.

Statement 1

So the four points A, B, C, D form a rectangle. We are not given any particular order first of all, so we dont know whether we should make this rectangle as ABCD or ACDB or something else.
Even if we make the cyclic order ABCD, then in that case opposite sides AB and CD will be equal, but whether adjacent sides AB and BC are equal is something that depends on whether this rectangle is also a square. This is not given. So we cannot conclude in this case whether AB = BC.
If we cannot conclude in this one case then there is no point in taking other cases like ACDB etc. So not sufficient.

Statement 2

AB is not equal to AC, but this doesnt tell us anything about AB and BC. So not sufficient.

Combining the two statements,

I) If we take a rectangle in this order: ABCD - here opposite sides AB=CD and AD=BC. Now if its adjacent sides are equal (its a square) then AB=BC. We are given from statement 2, AB is not equal to AC. But AB and AC can anyway not be equal because AB is a side and AC is a diagonal. Diagonal > Side anyway. We are not given whether its a square or just a rectangle so we cannot conclude whether AB=BC or not.

We can take other order for rectangle also: ADCB or ACBD but that is not required because for order ABCD only we are unable to conclude anything about the question asked. So this is not sufficient.