Final answer:
Using the properties of an isosceles triangle, where two sides are equal, the length of HI should be equal to IG which is 11 units. However, the provided answer choices do not include this length, indicating a potential error in the question or choices.
Step-by-step explanation:
In triangle GHI, where angle H is congruent to angle G, and the lengths of IG and GH are given as 11 units and 14 units respectively, we can determine the length of HI by using the properties of isosceles triangles. Since angle H is congruent to angle G, we know that the triangle is isosceles and the sides opposite these angles, namely IG and GH, must be equal. This indicates that GH also measures 11 units, as does IG. However, the options provided in the question do not take into account this property, as neither 3, 2, nor 23 are equal to 11. The closest option to the correct calculation based on the isosceles triangle properties would be 11 units, none of the choices listed are correct if the triangle is truly isosceles as described. This may be due to a typographical error in the question or choices provided.