Question

statement
1 (overline{gh}paralleloverline{ef})
2 (overline{fg}perpoverline{ef})
3 (overline{gh}perpoverline{eh})
4 (angle fcongangle h)
5 (angle fegcongangle egh)
6 (overline{eg}congoverline{eg})
7 (\triangle efgcong\triangle ghe)

Explanation:

Step1: Recall triangle congruence theorems

We have two right - angled triangles \(\triangle EFG\) and \(\triangle GHE\). We know that \(\angle F=\angle H\) (right angles), \(\angle FEG = \angle EGH\) (alternate interior angles as \(GH\parallel EF\)), and \(EG = EG\) (common side).

Step2: Apply the AAS (Angle - Angle - Side) theorem

The AAS (Angle - Angle - Side) congruence theorem states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent. In \(\triangle EFG\) and \(\triangle GHE\), we have two pairs of congruent angles (\(\angle F=\angle H\) and \(\angle FEG=\angle EGH\)) and a pair of congruent non - included sides (\(EG = EG\)).

Answer:

AAS