The diagram shows that ∠HGI ≅ ∠JGI and ∠GIH ≅ ∠GIJ. What additional congruence statement can be made based on this diagram?

Answer 1

Given the angles you've noted from the diagram—specifically the relationships that \( \angle HGI \cong \angle JGI \) and \( \angle GIH \cong \angle GIJ \)—we can infer a congruence relationship involving the triangles formed by these angles.

Since \( \angle HGI \cong \angle JGI \) and \( \angle GIH \cong \angle GIJ \), we can establish that:

1. The triangles \( \triangle HGI \) and \( \triangle JGI \) share a common angle \( \angle G \) (which is \( \angle GIG \)).

Using the Angle-Angle (AA) similarity criterion (or congruence by two angles), we can assert that the two triangles are congruent due to having two pairs of angles congruent:

\[ \triangle HGI \cong \triangle JGI \]

Thus, an additional congruence statement that can be made is:

\[ \triangle HGI \cong \triangle JGI \]