Question

what additional information is needed to prove the 2 triangles are congruent by the listed theorem?
\\( \overline { m k } = \overline { g i } \\)
\\( \angle m l k = \angle g h i \\)
\\( \angle g i h = \angle m k l \\)

Explanation:

Step1: Recall SAS (Side - Angle - Side) Congruence Criterion

SAS states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Analyze the Given Sides

In \(\triangle LMK\) and \(\triangle IGH\), we already have two pairs of equal sides (as indicated by the marks in the figure). For SAS, we need the included angles.
The included angle for the sides in \(\triangle LMK\) is \(\angle MKL\) and for the sides in \(\triangle IGH\) is \(\angle GIH\).

Answer:

\(\angle GIH=\angle MKL\)