Question

please answer. ABCD is a quadrilateral in which AC and BD are its diagonals. prove that AB+BC+CD+DA>AC+BD

Answer 1

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

In triangle ACB, AB + BC > AC...... 1

In triangle BDC, BC + CD > BD...... 2

In triangle ACD, AD + DC > AC...... 3

In triangle BAD, AB + AD > BD....... 4

Adding 1,2,3 and 4,

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

2AB + 2BC + 2CD + 2AD > 2AC + 2BD

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