HGI is congruent to JIG due to the Side-Side-Side congruence theorem.
This theorem states that if the three sides of one triangle are congruent to the three sides of another triangle, the triangles must be congruent.
In order to create these triangles, we must draw a diagonal in this triangle. This will be a shared side between both triangles.
A rectangle's opposite sides are congruent; this means the top and left sides, which are part of one triangle, will be congruent to the bottom and right sides, which are part of the other triangle.
This gives us all 3 sides of both triangles congruent, and therefore the congruence theorem applies.
