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In the figure above, three segments are drawn from the oppos

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In the figure above, three segments are drawn from the opposite vertic  [#permalink]

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New post 18 Sep 2011, 00:08
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In the figure above, three segments are drawn from the opposite vertices of a hexagon to form six triangles. These segments all bisect each other at point A. Are all of the triangles equilateral?

(1) All six sides of the hexagon are the same length.
(2) The three segments drawn between the opposite vertices are the same length are are bisected by point A.


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Re: In the figure above, three segments are drawn from the oppos  [#permalink]

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New post 27 Aug 2013, 15:21
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I try to visualize the question as following:

Note: if all six triangles in a hexagon are equilateral, then the hexagon has all equal sides and six 120 degrees internal angles. The hexagon is regular.
If the hexagon has only six equal sides, the hexagon may not be regular. Thus, six triangles may not be equilateral.

Answer is C.

Hope it helps.
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Re: In the figure above, three segments are drawn from the opposite vertic  [#permalink]

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New post 18 Sep 2011, 00:40
Given: The segments bisects each other at point A.

In this question, we need to know two things.

1. Whether the segments(diagonals) are of same length.
2. Whether the angles formed by the edges of the hexagon are same.

I. All six sides are of same length. -> Not Sufficient. This info doesn't tell us whether the triangles are equilateral.

II. The three segments(diagonals) are of same length. Not Sufficient. We do not know whether the lengths of the edges are equal.

I & II, both are sufficient. It is because -

1. When the six edges are equal, the angle formed by one edge at the centre is 180 - 2x, x is the angle which is opposite to the side formed by half of a segment in a particular triangle.

2. Let's take 180 - 2x = Y.Now there are 6 angles, each measuring Y and 6Y = 360 => Y = 60 degree.

Then its easy to say the triangle are equilateral.
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Re: In the figure above, three segments are drawn from the opposite vertic  [#permalink]

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New post 21 Sep 2011, 23:38
a gives that all triangles are similar,however the hexagon side and the two bisected sides don't have relation specified. not sufficient.

b no mention about the hexagon sides. not sufficient.


a+b

all sides are equal.hence equilateral.

C it is.
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Re: In the figure above, three segments are drawn from the opposite vertic  [#permalink]

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New post 22 Sep 2011, 01:44
This question is from 800score. I did this few days ago.
Here you can check illustrative solution in flash
http://www.800score.com/explanations/GMAT_MATH_T1_Q25_Hard.html
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In the figure above, three segments are drawn from the oppos  [#permalink]

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In the figure above, three segments are drawn from the opposite vertices of a hexagon to form six triangles. These segments all bisect each other at point A. Are all of the triangles equilateral?

(1) All six sides of the hexagon are the same length.
(2) The three segments drawn between the opposite vertices are the same length are are bisected by point A.
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Originally posted by vaishnogmat on 26 Aug 2013, 22:18.
Last edited by Bunuel on 27 Aug 2013, 03:25, edited 1 time in total.
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Re: Equilateral triangles in Hexagon?  [#permalink]

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New post 27 Aug 2013, 00:00
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Experts kindly correct me if my thinking process is incorrect.

From the properties of hexagon, if all the interior angles are equal and if all the sides are equal, then it's a regular hexagon and a regular hexagon could be divided into six equilateral triangles. Hence by proving our hexagon as regular hexagon, we should get our answer.

Option 1: Although it is given that all six sides of the hexagon are equal, with no information about the angles or the positioning of the bisectors, we couldn't conclusively say it's a regular hexagon. hence, not sufficient.

Option 2: Not sufficient

Option 1 & 2: Will prove the hexagon is definitely a regular hexagon.
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Re: In the figure above, three segments are drawn from the oppos  [#permalink]

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New post 29 Aug 2013, 03:30
pqhai wrote:
I try to visualize the question as following:

Note: if all six triangles in a hexagon are equilateral, then the hexagon has all equal sides and six 120 degrees internal angles. The hexagon is regular.
If the hexagon has only six equal sides, the hexagon may not be regular. Thus, six triangles may not be equilateral.

Answer is C.

Hope it helps.


I couldn't visualize this and hence couldn't come up with a proper draw, but this helps, thanks.
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Re: In the figure above, three segments are drawn from the oppos  [#permalink]

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New post 10 Dec 2013, 09:51
hey guys. i found an excellent explanation of this problem http://www.800score.com/explanations/GM ... _Hard.html
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Re: In the figure above, three segments are drawn from the oppos  [#permalink]

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New post 04 Feb 2015, 12:52
Hi All,

The explanation/drawings offered by pqhai for this question are spot-on, so I won't rehash any of that work here. Instead, I'll focus on a 'key' element to dealing with DS questions: to get the correct answer, you have to be clear on what you KNOW and what you DON'T KNOW.

This prompt starts us off with a hexagon, which is a 'weird' shape (and is not likely to show up on Test Day). Before dealing with this shape, I'm going to start with an easier example:

If you're given a triangle, what do you really KNOW about the triangle?
1) You know it has 3 sides
2) You know that its 3 angles add up to 180 degrees
3) You know that the length of the sides are related (through the triangle inequality theorem)
4) You know that the biggest side is 'across' from the biggest angle, the smallest is across from the smallest.

What do you NOT KNOW:
1) You DON'T KNOW the lengths of the sides.
2) You DON'T KNOW the angles
3) You DON'T KNOW if it's a right triangle, isosceles, equilateral, etc.
Etc.

Now, take that same perspective with this prompt. We're given a hexagon, so what do you really KNOW about it?
1) A hexagon has 6 sides
2) A hexagon has 720 degrees

What do we NOT KNOW:
1) We don't know if the sides are the same length.
2) We don't know any of the angles.

Realizing those points, working through the rest of the question isn't that tough. Most of the 'work' is really about drawing pictures and considering the various possibilities. In all DS questions, make note of the things that you don't know (and the possibilities that can occur) and you'll be better able to get to the correct answer (and have proof of it).

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Re: In the figure above, three segments are drawn from the oppos  [#permalink]

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New post 03 Nov 2018, 08:50
QUOTE: (2) The three segments drawn between the opposite vertices are the same length are are bisected by point A.

WHAT?
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Re: In the figure above, three segments are drawn from the oppos  [#permalink]

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New post 03 Nov 2018, 23:41
Hello,

How I took this question is as below.
Given: A hexagon which is divided by 3 segments which bisect each other at point A. And this 3 segment make 6 triangles.
Question: Are these triangles are equilateral.

Statement 1
All the sides of hexagon are equal.
then angle substanded at A in front of all sides will be equal.
Now suppose if length of any of 3 segments remain unequal, will length of hexagon side will remain same? I think NO.
So when it is given that all sides are equal in hexagon, other two sides made by intersection of segments have to be equal to side of hexagon.
In this way all triangles must be equilateral.

Statement 2
All segments are equal in length.
Now, in this case two sides made by segments will be equal. Third side (Hexagon's side) could be or couldn't be equal to sides drawn by segments.

A seems correct answer.
Now please tell me where I did wrong.

subhajeet wrote:
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In the figure above, three segments are drawn from the opposite vertices of a hexagon to form six triangles. These segments all bisect each other at point A. Are all of the triangles equilateral?

(1) All six sides of the hexagon are the same length.
(2) The three segments drawn between the opposite vertices are the same length are are bisected by point A.


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Re: In the figure above, three segments are drawn from the oppos  [#permalink]

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New post 04 Nov 2018, 08:18
gmatzpractice wrote:
QUOTE: (2) The three segments drawn between the opposite vertices are the same length are are bisected by point A.

WHAT?


Typo:
(2) The three segments drawn between the opposite vertices are the same length AND are bisected by point A.

(1) is not sufficient. Imagine it's a beach ball.
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Re: In the figure above, three segments are drawn from the oppos   [#permalink] 04 Nov 2018, 08:18
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