Label the corners of the square A,B,C,D with AC as a diagonal.
Draw diagonal AC. Triangle ACD is one of the four triangles and has angles 45, 45, 90.
Next choose point E on AC so that BC=CE and draw EB. BCE is the second triangle, with angles 45, 67.5, 67.5.
Next find point F on AB so that EF is perpendictular to AC, and draw EF. The angles of AEF are 45, 45, 90 (AEF is much smaller than ACD) and the angles of BEF are 22.5, 22.5, 135.
Triangles ACD, BCE, AEF, and BEF are all isosceles and none of them are congruent.
Jer provides an interesting six triangle dissection here. |
