TITLE: Can every triangle be divided into five isosceles triangles?
QUESTION [5 upvotes]: That's my problem: Can every triangle be divided into five isosceles triangles?
I've got to give evidence why this is true or not true...
(sorry for possible language mistakes - I'm from Germany)
Thanks in advance 
Markus

REPLY [2 votes]: It is possible to divide a triangle into five isosceles triangles. This is provable by induction. The fact that all right triangles are 2-dissectible is important because every triangle can be divided into two right triangles by cutting along the altitude to its longest side. Each can then be cut into two isosceles triangles by cutting along the median from the right angle to the hypotenuse. 
Hence using this we can prove that any triangle can be divided to 4 isosceles triangles. Further we use this to prove that any triangle can be divided to 5 isosceles triangles. 
To prove it draw a line from any of the vertex to opposite side to get triangles. One of them will be isosceles. Consider other as new starting triangle and based on above proved theorem that any triangle can be divided to 4 isosceles triangles we get 4 isosceles triangles from other part of original triangle
Hence giving in total 5 isoceles triangles. Please feel free to ask if you are little confused over this description.