## pratu043 3 years ago Show that in a quadrilateral ABCD, AB+BC+CA+DA > AC+BD.

1. mukushla

|dw:1344502321128:dw|

2. sauravshakya

|dw:1344502527479:dw|

3. sauravshakya

take two triangles ABC and triangles BDC

4. sauravshakya

|dw:1344502571798:dw|In triangle ABC,

5. sauravshakya

I think the question is AB+BC+CA+DA > AC+CD

6. mukushla

@pratu043 i think there is a problem with question

7. mukushla

AB+BC+CA+DA > AC+BD --- ---

8. sauravshakya

@pratu043 u there

9. pratu043

Sorry, it is BD not CD.

10. pratu043

11. sauravshakya

oh i got it

12. sauravshakya

in triangle ABD , AB + DA > BD

13. pratu043

The quadrilateral should be like this: |dw:1344503679049:dw|

14. sauravshakya

in triangle ABD , AB + DA > BD right @pratu043

15. pratu043

How did you get that @sauravshakya?

16. sauravshakya

In a triangle sum of two sides of a triangle is always greater than the third side right?

17. sauravshakya

@pratu043

18. pratu043

Oops, yes I forgot that.

19. pratu043

So what next?

20. sauravshakya

Cancel CA and AC since they are same side..... so u will get AB+BC+DA > BD.

21. sauravshakya

right?

22. sauravshakya

and since AB + BC > BD, AB+BC+DA > BD (thus, proved)

23. sauravshakya

got it?

24. pratu043

But AB+BC+DA > BD is not what we should prove.

25. jiteshmeghwal9

|dw:1344516745619:dw|