Loser66
  • Loser66
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
Mathematics
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SOLVED
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katieb
  • katieb
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Loser66
  • Loser66
@dan815 What do they want me to do?
dan815
  • dan815
no not all triangles are isocles
Loser66
  • Loser66
dan!! of course.

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dan815
  • dan815
lol
Loser66
  • Loser66
but I don't understand the rest of the question.
dan815
  • 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
Loser66
  • Loser66
a right triangle is a perfect proof, right?
Loser66
  • 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?
anonymous
  • anonymous
dan
Loser66
  • Loser66
???
anonymous
  • anonymous
@Loser66 this is not trivial question. it has geometrical attempt
anonymous
  • anonymous
This fallacy has been attributed to Lewis Carroll znd explained by maxwell .
anonymous
  • anonymous
https://en.wikipedia.org/wiki/Mathematical_fallacy#Fallacy_of_the_isosceles_triangle
anonymous
  • anonymous
if you need any help understanding the proof and the fault in it im always here :P
Loser66
  • Loser66
hey, ikram. What should I do for this question? find out the fallacy?
Loser66
  • 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?
anonymous
  • 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.
Loser66
  • Loser66
ok, Thanks a ton. Let me try. :)
anonymous
  • anonymous
in this case its okay if used Internet as reference since this is history and not work like its wrong proof anyway lol
anonymous
  • 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 ?
anonymous
  • anonymous
you also can disprove the main question in addition of mention history about it :D
Loser66
  • 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?
Loser66
  • Loser66
It means the side must be between the angles.
anonymous
  • anonymous
nope, the mistake is in step 3
anonymous
  • 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.
anonymous
  • 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
Loser66
  • Loser66
oh, I see!! man!!
anonymous
  • anonymous
:D

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