I strongly suspect that the only solution in the congruent case is a 30-60-90 triangle dissected by the perp bisector of the hypotenuse, and the angle-bisector of the 60 angle. /| / | / | / | / | /_____| / \ | / \ | / \ | - \ | - \| Rough heuristic: two congruent triangles fit together to form a parallelogram or kite [since if two edges are to fit against one, rriangle wd be degenerate]. Only in the latter case can the quadrilateral be completed to a triangle. R. On Mon, 21 Jan 2008, Dan Asimov wrote:
Michael writes:
<< Dan Asimov wrote:
Determine which shape(s) of triangles, if any, can be dissected into 3 congruent triangular pieces.
Then do the same for 3 *similar* triangles.
Huh? You can cut any right triangle into 2 similar triangles, then do this again to one of these, resulting in the original triangle cut into 3 similar ones.
--Dan
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