abcd is a quadrilateral. prove that ab +bc+cd+da>ac+bd
Answers
Answered by
1
ABCD is a quadratilateral .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 we get.
AB + BC + BC + CD + AD + DC + AB + AD > AC + BD + AC + BD
2AB + 2BC + 2CD + 2AD > 2AC + 2BD
AB + BC + CD + AD > AC + BD.
Attachments:
Similar questions