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In the figure above, three segments are drawn from the oppos [#permalink]
26 Aug 2013, 21:18

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

85% (hard)

Question Stats:

28% (02:06) correct
72% (00:59) wrong based on 57 sessions

Attachment:

File comment: Image

Hexagon.png [ 4.42 KiB | Viewed 867 times ]

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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Last edited by Bunuel on 27 Aug 2013, 02:25, edited 1 time in total.

Re: Equilateral triangles in Hexagon? [#permalink]
26 Aug 2013, 23:00

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.

Re: In the figure above, three segments are drawn from the oppos [#permalink]
27 Aug 2013, 14:21

4

This post received KUDOS

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.

Attachments

Hexagon.jpg [ 58.69 KiB | Viewed 775 times ]

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Re: In the figure above, three segments are drawn from the oppos [#permalink]
29 Aug 2013, 02:30

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.