By comparing the lengths of the sides of the two triangles, ABC and DEF, formed by the points we can find the relationship (if any) between them, using the distance formula:
AB=√((5-1)2+(5-4)2)=√(16+1)=√17;
DE=√((-1-(-5))2+(0-1)2)=√((-1+5))2+(-1)2)=√(16+1)=√17.
Therefore AB=DE.
AC=√((2-1)2+(2-4)2)=√(1+4)=√5;
DF=√((-4-(-5))2+(3-1)2)=√((-4+5))2+(2)2)=√(1+4)=√5.
Therefore AC=DF.
BC=√((2-5)2+(2-5)2)=√(9+9)=√18;
EF=√((-4-(-1))2+(3-0)2)=√((-4+1))2+(3)2)=√(9+9)=√18.
Therefore BC=EF.
So the triangles are congruent.