# 4.  ABCD is a quadrilateral.         Is  $\small AB+BC+CD+DA> AC+BD$ ?

As we know that the sum of two sides of ANY triangle is always greater than the third side(Triangles Inequality Rule).

So,

In $\small \Delta ABC$ :

$\overline {AB}+\overline {BC}>\overline{AC}...........(1)$

In $\small \Delta CDA$ :

$\overline {CD}+\overline {DA}>\overline{BD}...........(2)$

Adding (1) and (2) we get,

$\small AB+BC+CD+DA> AC+BD$

Hence The given statement is True.

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