Question

in △fgh, ∠f ≅ ∠h, hf = 13 and gh = 11. find fg.

Explanation:

Step1: Identify the triangle type

In $\triangle FGH$, $\angle F \cong \angle H$. By the Isosceles Triangle Theorem, if two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Step2: Determine the opposite sides

The side opposite $\angle F$ is $GH$, and the side opposite $\angle H$ is $FG$. Since $\angle F \cong \angle H$, we have $FG = GH$.

Step3: Substitute the given value

We know that $GH = 11$, so $FG = 11$.

Answer:

$FG = \boxed{11}$