Question

show that in aquadrilateral ABCD ab+ bc + cd+ da greater than ac+ bd

Answer 1

ABCD is a quadrilateral.
AC and BD are diagonals.

 We know that the sum of two sides of a 
triangle is greater than the third side.
In△ACB, we have:
AB+BC>AC     ...(1)
In △BDC, we have:
BC+CD>BD     ...(2)
In △ACD, we have:
AD+DC>AC      ...(3)
In △BAD, we have:
AB+AD>BD       ...(4)
Adding (1), (2), (3) & (4), we get:AB+BC+BC+CD+AD+DC+AB+AD>
AC+BD+AC+BD
⇒2AB+2BC+2CD+2AD>2AC+2BD
⇒AB+BC+CD+AD>AC+BD