Question

ABCD is a quadrilateral prove AB+BC+CD+DA>AC+BD

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Answer 1

I hope the it is known to you that sum of lengths of two sides of a triangle is grater than the length of third side. using this we can prove that the answer to your question is yes.

AB + BC > AC

AC + CD > BD

CD + AD > AC

AB + DA > BD

ADDING THE FOUR WE GET

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

DIVIDING BY 2

WE GET

AB + BC + CD + DA > AC + BD

Hope that this answer will help you ✌️