Question

if \\(\overline{fg} \cong \overline{fi}\\) and \\(gh = 76\\), what is \\(hi\\)?
\\(hi = \square\\)

Explanation:

Step1: Identify congruent triangles

We can see that $\triangle HFG$ and $\triangle HFI$ are right triangles, with $\overline{FG} \cong \overline{FI}$, and $\overline{HF}$ is a common side. By the HL (Hypotenuse-Leg) congruence theorem for right triangles, $\triangle HFG \cong \triangle HFI$.

Step2: Corresponding sides are equal

Since corresponding sides of congruent triangles are congruent, $\overline{GH} \cong \overline{HI}$.

Step3: Substitute given value

Given $GH = 76$, so $HI = GH$.
$HI = 76$

Answer:

76