(RS)² = ( 0 - 4 )² + ( - 3 + 5 )²  = ( - 4 )² + 2² = 16 + 4 = 20

RS = √20

(RT)² = ( 6 - 4 )² + ( - 9 + 5 )² = 2 ² + ( -4 )² = 4 + 16 = 20

Rt = √20

(TS)² = ( 6 - 0 )² + ( - 9 + 3 )² = 6² + ( - 6 )²= 36 + 36 = 72

TS = √72

ES  =  RT  , le triangle est isocèle

( EF)² = ( - 6 + 1 )² + ( 2 - 0 )² = ( - 5 )² + 2² = 25 + 4 = 29

EF = √29

(FG)² = ( 1 + 6 )² + ( 5 - 2 )² = 7 ² + 3 ² = 49 + 9 = 58

FG = √58

(EG)² = ( 1 + 1 )² + ( 5 - 0 )² = 2 ² + 5 ² = 4 + 25 = 29

EG = √29

√29 + √29 = √58

le triangle est rectangle et isocèle