Question

ABCDis a quadrilateral is AB+BC+CD+DA>AC+BD?

Answer 1

we can do this by :

join the diagonals of the quad.ABCD(both the diagonals)

then,we will have 2 triangles

tri(abc)and tri(adc)

thus ,the sum of any two side of a triangle is greater than the third side.

hence, AB+BC>AC

similarly,AD+CD>AC

NOW,wecan prove by the diagonal BD

that,AB+AD>BD

andBC+CD>BD

BY ADDING,

2(AB+BC+CD+DA)>2(AC+BD)

BY CANCELLING 2

WE get,AB+BC+CD+DA>AC+BD

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