The additional information to complete the congruence by ASA congruence theorem is
GH ≅ HC
How to find the additional information
The ASA congruence theorem requires that two angles and the included sides of both triangles being considered are congruent.
In this case, the used parts are
angle G ≅ angle C - given
GH ≅ HC - included side
GHI ≅ EHC - vertical angle theorem