## Loser66 one year ago Is it true that all triangles are isoceles? If you think this is a trivial question, explain the hidden assumption in the proof that all triangles are isoceles. Please, help

1. Loser66

@dan815 What do they want me to do?

2. dan815

no not all triangles are isocles

3. Loser66

dan!! of course.

4. dan815

lol

5. Loser66

but I don't understand the rest of the question.

6. dan815

to show that not all triangles are isocles, pick 3 non equal angles that sum to 180, and prove that a different angle has a different side

7. Loser66

a right triangle is a perfect proof, right?

8. Loser66

So, If I say: No, not all triangles are isoceles, and give out the proof, I don't have to do the rest of it, right?

9. anonymous

dan

10. Loser66

???

11. anonymous

@Loser66 this is not trivial question. it has geometrical attempt

12. anonymous

This fallacy has been attributed to Lewis Carroll znd explained by maxwell .

13. anonymous
14. anonymous

if you need any help understanding the proof and the fault in it im always here :P

15. Loser66

hey, ikram. What should I do for this question? find out the fallacy?

16. Loser66

Since this proof is not on my book, and I am not allowed to use the internet solution, how can I prove it is a fallacy?

17. anonymous

yes, just mention their used to be a known proof by Lewis Carroll , which says " every triangle is isosceles ", mention the proof and then say why its wrong.

18. Loser66

ok, Thanks a ton. Let me try. :)

19. anonymous

in this case its okay if used Internet as reference since this is history and not work like its wrong proof anyway lol

20. anonymous

you are welcome @Loser66 :) PS:- saying every triangle is isosceles s not weird at all, even if you see some triangles do not match, one of eclids postulate said "all right triangles are congruent" and have a proof for it even thought for first look it does not seems alright, okay now ?

21. anonymous

you also can disprove the main question in addition of mention history about it :D

22. Loser66

I figure out the mistake on the proof. Correct me if I am wrong, please at 6, the case to get 2 triangles are equal is ASA, not AAS, right?

23. Loser66

It means the side must be between the angles.

24. anonymous

nope, the mistake is in step 3

25. anonymous

Let these two lines meet at a point O., there is no guaranty that O would be inside the triangle not on circumcircle or out of it.

26. anonymous

in general thes line meet in this conditional at point O in circumcircle, there is only one case that it would be inside the triangle which is isosceles and equilateral triangles

27. Loser66

oh, I see!! man!!

28. anonymous

:D