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Get Answers to all your Questions
Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD
Answers (1)
Given, ABCD is a quadrilateral
To Prove : AB + BC + CD + DA > AC + BD
Proof - Since, we know that sum of the two sides of a triangle is greater than the third side.
In ABC, AB + BC > AC
In BCD, BC + CD > BD
In CAD, AD + CD > AC
In BAD, BA + AD > BD
Adding all the above equations,
2(AB + BC + CA + AD) > 2(AC + BD)
2(AB + BC + CA + AD) > 2(AC + BD)
AB + BC + CA + AD > AC + BD
Hence, proved.
View full answer
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