Question

In triangle, F, G, H, comma△FGH, angle, F, \cong, angle, H, comma∠F≅∠H, H, F, equals, 13HF=13 and G, H, equals, 11GH=11. Find F, G, .FG

Answer 1

In triangle \( \triangle FGH \), you are given that \( \angle F \cong \angle H \). This means that \( \triangle FGH \) is isosceles, with \( F \) and \( H \) being the vertex angles. Therefore, the sides opposite to these angles are equal:

\[
FG = GH
\]

You are given the lengths of sides \( HF \) and \( GH \):

- \( HF = 13 \)
- \( GH = 11 \)

Since \( FG \) and \( GH \) have to be equal, we focus on \( FG \):

\[
FG = GH
\]
Thus, since \( GH = 11 \),

\[
FG = 11
\]

So, the length of \( FG \) is:

\[
\boxed{11}
\]