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  • ABCD is a quadrilateral. Is AB + BC + CD + DA > AC + BD?

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

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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.

 

Posted by

Pankaj Sanodiya

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