Question

In a quadrilateral ABCD, prove that
AB + BC + CD is greater than DA

Answer 1

ABCD is a quadrilateral so divide it into 4 triangles.
Now consider the triangle ABC
AB + BC > AC...................................................EQUATION (1)
And now if CD is added to both the sides,we get
AB + BC + CD > AC +CD

Now consider the triangle ACD
AC + CD > AD ..................................................Equation(2)
From equation (1) and (2) we get
AB +BC +CD +DA

Now consider the triangle ABC
AB +BC>Ac.......................................................Equation(3)

Now consider the triangle ACD
CD +DA >AC...................................................Equation(4)

Now  by adding equation (3) and (4) we get
AB +BC+CD+DA >AC+AC  that will give you
AB+BC+CD+DC>2AC

You can understand this answer diagramatically!!................
Hope this helps u..................................^_^

Answer 2

Answer:

ABCD is a quadrilateral so divide it into 4 triangles.

Now consider the triangle ABC

AB + BC > AC...................................................EQUATION (1)

And now if CD is added to both the sides,we get

AB + BC + CD > AC +CD

Now consider the triangle ACD

AC + CD > AD ..................................................Equation(2)

From equation (1) and (2) we get

AB +BC +CD +DA

Now consider the triangle ABC

AB +BC>Ac.......................................................Equation(3)

Now consider the triangle ACD

CD +DA >AC...................................................Equation(4)

Now  by adding equation (3) and (4) we get

AB +BC+CD+DA >AC+AC  that will give you

AB+BC+CD+DC>2AC

hope so it helps u

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