Question

complete the proof that \\(\overline{gh} \cong \overline{ij}\\).
(image of triangle khi with segment gj parallel to hi, and a table with statements and reasons for the proof steps, ending with step 15: \\(\overline{gh} \cong \overline{ij}\\) needing a reason)

Explanation:

Step1: Recall the definition of congruent segments

If two segments have the same length, then they are congruent. This is the definition of congruent segments: If \( AB = CD \), then \( \overline{AB} \cong \overline{CD} \).

Step2: Apply the definition to \( GH \) and \( IJ \)

We have already proven in step 14 that \( GH = IJ \). By the definition of congruent segments, if the lengths of two segments are equal, the segments themselves are congruent. So, since \( GH = IJ \), we can conclude that \( \overline{GH} \cong \overline{IJ} \).

Answer:

Definition of Congruent Segments (or: If two segments have equal length, then they are congruent)