A fur dresser had to put a patch shaped like a scalene triangle on a piece of fur. Suddenly he realized he had made a terrible mistake. The patch fitted the hole but the fur side faced the wrong way.
The fur dresser, after some thought, cut the triangular patch into 3 parts, each of which would be unchanged when turned over. How?
Let ABC be the triangle with C being the largest angle.
Construct the altitude perpendictular to AB (through C). Let D be the point at which the altitude intersects AB.
CAD and CBD are right triangles.
Let E be the midpoint of AC and F be the midpoint of BC.
Since E is the midpoint of the hypotenuse of CAD, EA=EC=ED and EAD is isosceles. Similarily, FB=FC=FD and FBD is isosceles.
The cuts can be made at DE and DF. EAD can be rotated so that EA coincides with EC and FBD can be rotated so that FB coincides with FC.