Question

ABCD is a quadrilateral. Prove that (AB+BC+CD+DA)> (AC+BD)

Answer 1

In the quadrilateral ABCD ab,bc,cd,da are the sides of the quadrilateral so AB+BC+CD+DA=ABCD. so statement 1 proved. here AC=AB+BC,BD=BC+CD Hence AC+BD=3sides but quadrilateral ABCD=4sides so,ABCD is greater than(AC+BD)

Answer 2

Answer:

Step-by-step explanation:

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.