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Prove that in a quadrilateral ABCD,

AB + BC + CD > DA

'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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,120

hi

Split your quadrilateral into two triangles and use the triangle inequality twice.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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Tried...But how do I get rid of the diagonal in the equation?

'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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,840

You can do it like this:

CD<AC+AD<(AB+BC)+AD. Q.E.D

*Last edited by anonimnystefy (2012-11-05 01:40:45)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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Yes! Thanks to bob bundy and anonimnystefy

'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'

'Humanity is still kept intact. It remains within.' -Alokananda

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 14,840

You are welcome!

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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