Question

if m∠fgi = m∠hgi = 38° and fi = 34, what is hi? hi = \boxed{}

Explanation:

Step1: Identify congruent triangles

Since \( \angle FGI = \angle HGI = 38^\circ \), \( \angle GFI = \angle GHI = 90^\circ \) (right angles), and \( GI \) is common to both \( \triangle GFI \) and \( \triangle GHI \), by AAS (Angle - Angle - Side) congruence criterion, \( \triangle GFI \cong \triangle GHI \).

Step2: Use congruent triangle property

In congruent triangles, corresponding sides are equal. So, the side \( FI \) in \( \triangle GFI \) corresponds to side \( HI \) in \( \triangle GHI \). Given that \( FI = 34 \), we can conclude that \( HI=FI \).

Answer:

\( 34 \)