Question

given fh ⊥ gh, kj ⊥ gj
prove △fhg ~ △kjg
identify the steps that complete the proof

Explanation:

Step1: Reason for \(\angle FHG\cong\angle GJK\)

Since \(\angle FHG\) and \(\angle GJK\) are right angles (from steps 1 - 3), by the property that all right angles are congruent, we have \(\angle FHG\cong\angle GJK\).

Step2: Completing statement 6

From step 5 (definition of vertical angles) and step 6 (vertical angles theorem), the statement is \(\angle FGH\cong\angle KGJ\)

Step3: Reason for \(\triangle FHG\sim\triangle KJG\)

We have two pairs of congruent angles (\(\angle FHG\cong\angle GJK\) and \(\angle FGH\cong\angle KGJ\)). By the AA (Angle - Angle) similarity theorem, \(\triangle FHG\sim\triangle KJG\)

Answer:

1. All right angles are congruent.
2. \(\angle FGH\cong\angle KGJ\)
3. AA (Angle - Angle) similarity theorem