Final answer:
The proof involves congruent triangles and reason #6 likely refers to a triangle congruence postulate like ASA or SSS. Reason #7 is CPCTC, used to show congruent corresponding segments in congruent triangles.
Step-by-step explanation:
The question seems to be about a geometric proof regarding congruent segments represented by HI and GJ. Without a specific context or diagram, it's challenging to provide accurate proof. However, the acronyms provided (such as ASAS, SSS, ASA, and CPCTC) are common in geometry and stand for Angle-Side-Angle (ASA), Side-Side-Side (SSS), and Corresponding Parts of Congruent Triangles are Congruent (CPCTC). These are reasons used to establish the congruence of triangles or parts of geometric figures. Reason #6 might be a triangle congruence postulate such as ASA or SSS, suggesting that two triangles are congruent because they have two angles and the included side is congruent or three sides are congruent, respectively. Reason #7 is likely CPCTC, which is used to show that if triangles are congruent, then all their corresponding parts, including segments like HI and GJ, are also congruent.