ABCD is a quadrilateral. Is AB+BC+CD+DA>AC+BD ?
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not it is not working properly
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in triangle ABC
AB+BC>AC
in triangle ADC
AD+DC>AC
in triangle BCD
BC+CD>BD
in triangle BAD
BA+AD>BD
adding all these equations
AB+AB+BC+BC+CD+CD+AD+AD>BD+BD+AC+AC
2(AB+BC+CD+AD)>2(BD+AC)
therefore,
AB+BC+CD+AD>BD+AC
AB+BC>AC
in triangle ADC
AD+DC>AC
in triangle BCD
BC+CD>BD
in triangle BAD
BA+AD>BD
adding all these equations
AB+AB+BC+BC+CD+CD+AD+AD>BD+BD+AC+AC
2(AB+BC+CD+AD)>2(BD+AC)
therefore,
AB+BC+CD+AD>BD+AC
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