Question

ABCD is a quadrilateral show that a b + BC + CD + D A is equal to greater than AC + BD ​

Answer 1

ABCD is a quadrilateral. Joining A to C and B to D, we get triangles ABC, BCD, CAD and BAD. AC and BD are the diagonals. Sum of the two sides of a triangle is greater than the third side.

So, considering the triangles ABC, BCD, CAD and BAD, we get.

AB+BC>AC

CD+AD>AC

AB+AD>BD

BC+CD>BD

Adding all the above equations

2(AB+BC+CA+AD) >2(AC+BD)

=> 2(AB+BC+CA+AD) >2(AC+BD)

=> (AB+BC+CA+AD) >(AC+BD)

=> (AC+BD) <(AB+BC+CA+AD)