A certain triangle ABC can be divided into 5 triangles each similar to ABC.
What are the angles A,B,C and how is the triangle divided?

Note that the triangles do not need to be congruent, or all the same shape and size, but only similar, i.e. the same shape but any size.

So, for example, draw ABC as a 45-45-90 triangle, with A being the right angle.  Mark the center of each segment, call the point D, E, and F.  Now draw DEF.  There are now 4 congruent triangles each containing 1/4 of the original area and each being 45-45-90.

All that remains is to divide any one of the 4 triangle into 2 and we have 5 similar but not all congruent triangles.

Posted by Larry on 2011-09-06 22:22:09