Question

the diagram shows that ∠hgi ≅ ∠jgi and ∠gih ≅ ∠gij. what additional congruence statement can be made based on this diagram? (1 point) ∠h ≅ ∠j, gh ≅ gj, hi ≅ ji, gi ≅ gj

Explanation:

Step1: Recall triangle - congruence criteria

We know that $\angle HGI\cong\angle JGI$ and $\angle GIH\cong\angle GIJ$, and side $GI$ is common to both $\triangle GIH$ and $\triangle GIJ$. By the Angle - Angle - Side (AAS) or Angle - Side - Angle (ASA) congruence criteria, for $\triangle GIH$ and $\triangle GIJ$, we can prove their congruence.

Step2: Use congruent - triangle properties

If $\triangle GIH\cong\triangle GIJ$, then corresponding parts of congruent triangles are congruent (CPCTC). The corresponding sides to $HI$ and $JI$ are equal.

Answer:

$\overline{HI}\cong\overline{JI}$