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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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#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.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#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