Question

Prove that any three sides of a quadrilateral are together greater than
the fourth side.
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Answer 1

Answer:

ABCD is a quadrilatral.

Join any one of the diagonal, say BD.

We know that, in a triangle, sum of two sides is greater than the third side.

 

Now, in triangle ABD, we have:

AB + AD > BD         ... (1)

 

In triangle BDC, we have:

BD + CD > BC         ... (2)

 

Adding (1) and (2), we get,

AB + AD + BD + CD > BD + BC

AB + AD + CD > BC  (Subtracting BD from both sides)

 

Thus, we have proved that sum of three sides is greater than the fourth side

Answer 2

Step-by-step explanation:

This is the solution of the upgiven given