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

1

• Brainly User
2016-02-20T09:58:25+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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..................................^_^