Subdividing Triangles into Six Isosceles Triangles
All Triangles Can Be Subdivided into Six Isosceles Triangles
1- Construct incircle via angle bisectors; the points of tangency create first 3 isosceles triangles.
The tangents from an external point are congruent, making the triangles isosceles.
2- Construct perpendicular bisectors of center triangle; the intersection point,
called the circumcenter, creates the last 3 isosceles triangles, since two of the sides
of each of the triangles are radii of the incircle.
credit:
http://geminis.dma.ulpgc.es/aplaza/ficheros/investigacion/ficheros/pww1_jun07.pdf