Question

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

1. we know that ∠fhg ≅ ∠kjg

because
dropdown with options: they are acute angles, they are vertical angles, all right angles are congruent

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Explanation:

To determine why \(\angle FHG \cong \angle KJG\), we analyze the given information: both angles are right angles (90 degrees). By the definition of congruent angles, all right angles have the same measure (90°), so they are congruent. The option "they are acute angles" is incorrect because right angles are 90°, not acute (less than 90°). The option "they are vertical angles" is incorrect because vertical angles are formed by intersecting lines, and these angles are right angles from different right triangles, not vertical angles. Thus, the correct reason is "all right angles are congruent."

Answer:

all right angles are congruent