Specious proof that all triangles are equilateral

by Lewis Carrol

     
AP bisects / BAC
QN is the perpendicular bisector of BC
        Meet at N

      AR = AS
      QB = QC
      RQ = SQ
      / QRB = / QSC = 90°
      \ RB = SC
      \ AB = AC

Repeat with B as the apex, and
      BC = BA
      \ all triangles are equilateral.