Question

Q4-)ABCD IS A QUADRILATERAL.
IS AB+CD+DA>AC+BD?

Answer 1

ABCD is a quad.Its diagonals are AC and BD.

In triangle ACB, AB + BC > AC - .....eq. 1[IN A TRIANGE THE SUM TWO SIDES IS ALWAYS GREATER THAN THE THIRD SIDE]

In triangle BDC, BC + CD > BD - ......eq2

In triangle ACD, AD + DC > AC - ......eq3

In triangle BAD, AB + AD > BD - .....eq4

Adding 1,2,3 and 4,

AB + BC + BC + CD + AD + DC + AB + AD > AC + BD + AC + BD

2AB + 2BC + 2CD + 2AD > 2AC + 2BD(on canceling 2)

AB + BC + CD + AD > AC + BD.

PROVED