Bikerman

Here is a nice little 'proof' that all triangles are isosceles triangles......

(1) side BD = DC (construction)

angle BDG = CDG (right angles)

side GD = GD (common)

triangle BDG=CDG (SAS) ….. (1)

(2) angle FAG = EAG (construction)

angle AFG = AEG (right angles)

angle AGF = AGE (sum of angles)

triangle AFG = AEG (ASA) ….. (2)

(3) side BG = GC (corr. sides from 1)

side GF = GE (corr. sides from 2)

angle GFB = GEC (right angles)

triangle GFB=GEC (RHS) ….. (3)

(4) AF = AE (corr. sides from 2)

FB = FC (corr. sides from 3)

AB = AF + FB = AE + FC = AC

ABC is isosceles!

Therefore all triangles are isosceles.

(1) side BD = DC (construction)

angle BDG = CDG (right angles)

side GD = GD (common)

triangle BDG=CDG (SAS) ….. (1)

(2) angle FAG = EAG (construction)

angle AFG = AEG (right angles)

angle AGF = AGE (sum of angles)

triangle AFG = AEG (ASA) ….. (2)

(3) side BG = GC (corr. sides from 1)

side GF = GE (corr. sides from 2)

angle GFB = GEC (right angles)

triangle GFB=GEC (RHS) ….. (3)

(4) AF = AE (corr. sides from 2)

FB = FC (corr. sides from 3)

AB = AF + FB = AE + FC = AC

ABC is isosceles!

Therefore all triangles are isosceles.