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#1 2013-01-20 15:46:49
- Agnishom
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Trapped with this trapezium
In a trapezium ABCD, if AB||CD then AC² + BD² = BC² + AB² + 2•AB•CD
How?
Last edited by Agnishom (2013-01-20 15:48:11)
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65
#2 2013-01-20 20:53:14
- bob bundy
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Re: Trapped with this trapezium
hi Agnishom,
I haven't fully explored this yet; maybe later; but it has the look of several applications of the cosine rule. As no cos(X) terms exist they must be cancelling out. Remember that angle ABD = angle BDC because of the parallels.
http://www.mathsisfun.com/algebra/trig-cosine-law.html
So perhaps you could have a go yourself ? 
LATER EDIT:
I've tried what I suggested and reached a formula connecting AC, BD, BC, AB, CD. But it isn't this one:
AC² + BD² = BC² + AB² + 2•AB•CD
So I set up the diagram on Sketchpad and got (for my trapezium)
LHS = 162.86 and RHS = 193.64
Are you sure you've got the right identity ?
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#3 2013-01-20 22:25:18
- bobbym
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Re: Trapped with this trapezium
Hi Agnishom;
How?
You might have a hard time proving that because I have been playing with trapeziums in geogebra and I can not find a single one where that is true.
Did you copy the problem correctly? Or what am I missing?
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#5 2013-01-20 22:37:06
- bobbym
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Re: Trapped with this trapezium
Hi Bob;
Looks that way!
I have been looking at it for a long time, I wanted to be sure. I thought maybe I was doing something wrong.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#6 2013-01-20 22:44:41
- bob bundy
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Re: Trapped with this trapezium
hi bobbym
I thought maybe I was doing something wrong.
That's the difference between us then. I tend to blunder in and post anyway. I guess that's why my posts are full of corrections.
Four applications of the cosine rule does allow you to eliminate any angles and get an equation. It isn't that one; not even close.
That's as far as I've got.
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#7 2013-01-20 23:54:30
- bobbym
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Re: Trapped with this trapezium
Not so different. I blunder around plenty but Agnishom is usually careful.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#8 2013-01-21 00:04:22
- Agnishom
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Re: Trapped with this trapezium
Let me check....
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65
#9 2013-01-21 00:05:57
- Agnishom
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Re: Trapped with this trapezium
Sorry, it should have been AC² + BD² = BC² + AD² + 2•AB•CD
P.S.: I have a hint in my book. But I dont get it. Do you want it?
Last edited by Agnishom (2013-01-21 00:08:14)
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65
#10 2013-01-21 00:18:35
- bobbym
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Re: Trapped with this trapezium
Hi Agnishom;
That one I believe works, yes post the hint.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#11 2013-01-21 00:25:33
- Agnishom
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Re: Trapped with this trapezium
Let CD < AB,
Drop perpendiculars DE and CF from D and C respectively.
In ΔABC, angle B is acute
Therefore, AC^2 = BC^2 + AB^2 - 2*AB*AE
In ΔABD, angle A is acute
Therefore, BD^2 = AD^2 + AB^2 - 2*AB*AF
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65
#13 2013-01-21 07:25:15
- scientia
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Re: Trapped with this trapezium
Hence
Last edited by scientia (2013-01-21 07:26:55)
#14 2013-01-21 13:47:34
- Agnishom
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Re: Trapped with this trapezium
Got it .... Thanks
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -65