pratu043
Show that in a quadrilateral ABCD, AB+BC+CA+DA > AC+BD.



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mukushla
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dw:1344502321128:dw

sauravshakya
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dw:1344502527479:dw

sauravshakya
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take two triangles ABC and triangles BDC

sauravshakya
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dw:1344502571798:dwIn triangle ABC,

sauravshakya
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I think the question is AB+BC+CA+DA > AC+CD

mukushla
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@pratu043
i think there is a problem with question

mukushla
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AB+BC+CA+DA > AC+BD
 

sauravshakya
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@pratu043 u there

pratu043
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Sorry, it is BD not CD.

pratu043
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help please.

sauravshakya
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oh i got it

sauravshakya
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in triangle ABD , AB + DA > BD

pratu043
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The quadrilateral should be like this:
dw:1344503679049:dw

sauravshakya
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in triangle ABD , AB + DA > BD right @pratu043

pratu043
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How did you get that @sauravshakya?

sauravshakya
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In a triangle sum of two sides of a triangle is always greater than the third side right?

sauravshakya
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@pratu043

pratu043
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Oops, yes I forgot that.

pratu043
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So what next?

sauravshakya
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Cancel CA and AC since they are same side..... so u will get
AB+BC+DA > BD.

sauravshakya
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right?

sauravshakya
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and since AB + BC > BD,
AB+BC+DA > BD
(thus, proved)

sauravshakya
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got it?

pratu043
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But AB+BC+DA > BD is not what we should prove.

jiteshmeghwal9
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