Triangle: Very hard problem

[prokhaled]

If abc is triangle, the angles 1,2 and 3 are equal and the angles 4,5 and 6 are equal and the angles 7,8 and 9 are equal

prove that:
the triangle xyz is equilateral triangle

[opus]

The very hard part of your post is, WHAT is your exact question!

[prokhaled]

If abc is triangle, the angles 1,2 and 3 are equal and the angles 4,5 and 6 are equal and the angles 7,8 and 9 are equal

prove that:
the triangle xyz is equilateral triangle

click here to see shape:
http://vbs.8k.com/tra.gif

[Helger]

Hmm - is that flat (2D) or is it 3D? If it's 3D which lines are in the back and which to the front?



abc is equilateral since 1+2+3 = 4+5+6 = 7+8+9 = 60° so ab = ac = bc (1=2=3...=20°)

(for the following reasoning the angles don't really matter but for completeness...)

looking at axc: with 1=4 it follows that ax = cx (and with 1=4=20° the other angle is 180°-40° = 140°)

it also follows that cbz = bay = acx

so: cz = cx = bz = by = ay = ax (remaining angles = (180° - 20°)/2 = 80°)

it follows that czx = byz = axy

so that zx = xy = yz (angles: 360° - 140° - 2*80° = 60°)

q.e.d

Helger

[opus]

sorry for the last post, but at first the picture didn't show

[thinktank2]

abc is equilateral since 1+2+3 = 4+5+6 = 7+8+9 = 60° so ab = ac = bc (1=2=3...=20°)

Wrong assumption.

The question is

If abc is triangle, the angles 1,2 and 3 are equal and the angles 4,5 and 6 are equal and the angles 7,8 and 9 are equal

prove that:
the triangle xyz is equilateral triangle

In other words

a) 1=2=3
b) 4=5=6
c) 7=8=9

He never said that 1+2+3 = 4+5+6 = 7+8+9.
You are asked to prove that the given triangle is an equilateral triangle. And the very first step you are doing is..
assuming it an equilateral triangle.

[Helger]

hrmpf. might be true in a way LOL.

[sql_lall]

The picture doesn't work. I click on it then a page comes up saying i can't open it, it's forbidden. Can you just post the pic??

[prokhaled]

I Think that picture work now, I f It does not work tell me

[sql_lall]

I got this warning:

Forbidden
Remote Host: [208.185.127.161]

You do not have permission to access http://vbs.8k.com/tra.gif
Data files must be stored on the same site they are linked from.

Thank you for using FreeServers

[sql_lall]

Sorry 'bout that. I clicked on the origional link and it didn't work, so i typed in the URL and Hey presto!!

I think i can do it, but by tomorrow