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Math problem doubt - Hexagon

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by getk » Sun Oct 05, 2008 11:57 am
Three segments drawn between opposite vertices of a Hexagon are of the same length. I was thinking, then it should be regular hexagon.
Can you please explain if it can be any other type of hexagon? (i meant a non-regular one)
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by stop@800 » Sun Oct 05, 2008 9:15 pm
IMO NO

For regular figures
All angles has to be equal.
which we can easily violate in situation described by you.

Whats the answer you have?
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by getk » Mon Oct 06, 2008 3:07 am
i found this in 800score
They are saying that,
condition of all 3 diagonals being equal doesn't mean the hexagon is a regular hexagon..
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by mental » Mon Oct 06, 2008 4:42 am
AGREED WITH STOP
it need not be a reg hexagon

just draw three lines intersecting each other, ensuring that the angle between them is not same

simpler, draw three lines with different intersecting points.
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by getk » Mon Oct 06, 2008 12:15 pm
thanks mate.. that's easy to imagine..
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by artistocrat » Mon Oct 06, 2008 9:00 pm
easier still imagine a chain with six links of equal length. of course you can elongate the ring ;-)
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by Vemuri » Wed Apr 29, 2009 8:40 am
stop@800 wrote:IMO NO

For regular figures
All angles has to be equal.
which we can easily violate in situation described by you.

Whats the answer you have?
I agree that when all angles are equal, the hexagon can be called a regular hexagon. But, when the 3 diagonals drawn between opposite vertices of a hexagon are of equal length, won't the angles also automatically be equal? I am not able to contradict it. Can someone help explain this better?
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by dumb.doofus » Wed Apr 29, 2009 1:27 pm
Vemuri wrote:
stop@800 wrote:IMO NO

For regular figures
All angles has to be equal.
which we can easily violate in situation described by you.

Whats the answer you have?
I agree that when all angles are equal, the hexagon can be called a regular hexagon. But, when the 3 diagonals drawn between opposite vertices of a hexagon are of equal length, won't the angles also automatically be equal? I am not able to contradict it. Can someone help explain this better?
Food for thought: Two isosceles triangle having the two sides of equal lengths can have different angles. That's the same logic you need to apply here.. three diagonals can be of equal length but that doesnt mean that internal angles of the hexagon would all be 120 degrees. It all depends upon the angle of intersection of the diagonals..

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