Question

given: (overline{gh} parallel overline{ij}), (overline{gh} cong overline{ij}), (overline{gk} cong overline{il}) prove: (angle ihk cong angle gjl)

Explanation:

Step1: Prove \(\triangle GHK\cong\triangle IJL\)

Since \(\overline{GH}\parallel\overline{IJ}\), then \(\angle HGK=\angle JIL\) (alternate - interior angles). Given \(\overline{GH}\cong\overline{IJ}\) and \(\overline{GK}\cong\overline{IL}\), by the Side - Angle - Side (SAS) congruence criterion, \(\triangle GHK\cong\triangle IJL\).

Step2: Use CPCTC

By the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) theorem, \(\angle IHK\cong\angle GJL\) (this is the statement for step 4).

Step3: For step 6

Since \(\angle IHK\) and \(\angle GJL\) are the angles we want to show congruent, and we have already established their congruence through the triangle congruence and CPCTC. The reason for step 6 could be "Definition of Congruent Angles" (if we are just restating the conclusion \(\angle IHK\cong\angle GJL\))

Answer:

1. \(\angle IHK\cong\angle GJL\)
2. \(\angle IHK\cong\angle GJL\) (statement); Definition of Congruent Angles (reason)