Question

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

Answer 1

@dan815 What do they want me to do?

Answer 2

no not all triangles are isocles

Answer 3

dan!! of course.

Answer 4

lol

Answer 5

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

Answer 6

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

Answer 7

a right triangle is a perfect proof, right?

Answer 8

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?

Answer 9

dan

Answer 10

???

Answer 11

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

Answer 12

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

Answer 13

https://en.wikipedia.org/wiki/Mathematical_fallacy#Fallacy_of_the_isosceles_triangle

Answer 14

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

Answer 15

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

Answer 16

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?

Answer 17

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.

Answer 18

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

Answer 19

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

Answer 20

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 ?

Answer 21

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

Answer 22

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?

Answer 23

It means the side must be between the angles.

Answer 24

nope, the mistake is in step 3

Answer 25

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.

Answer 26

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

Answer 27

oh, I see!! man!!

Answer 28

:D