Question

$\text{In q quadrilateral ABCD, show that (AB + BC + CD + DA)}>(AC+BD).$

Answer 1

ANSWER:
Given: Quadrilateral ABCD
To prove: (AB + BC + CD + DA ) > ( AC + BD )
Proof:In ∆ABC,AB+BC>AC
...iIn ∆CAD,CD+AD>AC
...iiIn ∆BAD,AB+AD>BD
...iiiIn ∆BCD,BC+CD>BD
Adding (i), (ii), (iii) and (iv), we get
2( AB + BC + CD + DA ) < 2( AC + BD)
Hence, (AB + BC + CD + DA ) < ( AC + BD).