State whether true or false
In a quadrilateral $A B C D$ ; $A B + B C + C D > D A$

True

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False

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Ambiguous

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Data insufficient

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Solution

The correct option is D True
$D r a w a d i a g o n a l A C t o t h e q u a d r i l a t e r a l . B y t r i a n g l e i n e q u a l i t y t h e o r e m I n △ A B C A C < A B + B C I n △ A D C A D < A C + C D (B y t r i a n g l e i n e q u a l i t y t h e o r e m) T h i s i m p l i e s A D < A B + B C + C D$
$⟹ D A < A B + B C + C D$

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Similar questions

A B C D

A B + B C + C D + D A > 2 B D

A B C D

A B + B C + C D + D A > 2 A C

A B C D, ∠ B = 90^{0}

∠ D = 90^{0}

2 A C^{2} - A B^{2} = B C^{2} + C D^{2} + D A^{2}

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