SOLUTION
From the question given, the reasons for the prove of the following statements are correct so far.
For the last part
[tex]\Delta GJK\cong\Delta IHK[/tex]
The reason is Side-side-side theorem.
This theorem states that all three sides of a triangle are congruent (identical) to the corresponding sides of another triangle, then the triangles themselves are also congruent.
Hence the answer is Side-side-side theorem.
