Question

given: ∠fhg and ∠kjg are right angles;
fh ≅ kj
prove: △fgh ≅ △kgj

1. partially visible because

all right angles are congruent

1. we know that ∠fgh ≅ ∠kgj

because they are
vertical angles.

1. △fgh ≅ △kgj because

dropdown options: aaa, aas, vertical angles are congruent
diagram: points f, h, g, j, k with right angles at h and j, fh and kj congruent (marked with ticks), vertical angles at g

Explanation:

Step1: Identify known congruences

We know \( \angle FHG \cong \angle KJG \) (right angles, all right angles congruent), \( \angle FGH \cong \angle KGJ \) (vertical angles, vertical angles congruent), and \( \overline{FH} \cong \overline{KJ} \) (given).

Step2: Determine triangle congruence criterion

The AAS (Angle - Angle - Side) criterion states that if two angles and a non - included side of one triangle are congruent to the corresponding two angles and non - included side of another triangle, then the triangles are congruent. Here, we have two angles (\( \angle FHG \cong \angle KJG \), \( \angle FGH \cong \angle KGJ \)) and a non - included side (\( \overline{FH} \cong \overline{KJ} \)) congruent between \( \triangle FGH \) and \( \triangle KGJ \). AAA (Angle - Angle - Angle) only shows similarity, not congruence. "Vertical angles are congruent" is a statement about angles, not a triangle congruence criterion. So the correct criterion is AAS.

Answer:

AAS