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

overline{hi} ≅ overline{ji}

overline{gi} ≅ overline{gi}

overline{gh} ≅ overline{gj}

Explanation:

Step1: Recall triangle - congruence criteria

We know that in \(\triangle HGI\) and \(\triangle JGI\), we have \(\angle HGI\cong\angle JGI\) and \(\angle GIH\cong\angle GIJ\), and \(GI = GI\) (common side). By the Angle - Angle - Side (AAS) congruence criterion, \(\triangle HGI\cong\triangle JGI\).

Step2: Use corresponding - parts of congruent triangles

If \(\triangle HGI\cong\triangle JGI\), then corresponding parts of congruent triangles are congruent. So, \(\angle H\cong\angle J\).

Answer:

\(\angle H\cong\angle J\)