Question

fg ≅ hi and fi ≅ gh. complete the proof that △fgh ≅ △hif.
statement
1 fg ≅ hi
2 fi ≅ gh
3
reason
given
given

Explanation:

Step1: Identify the common side

$\overline{FH}\cong\overline{HF}$ (Reflexive property of congruence)

Step2: Apply SSS congruence criterion

In $\triangle FGH$ and $\triangle HIF$, we have $\overline{FG}\cong\overline{HI}$ (given), $\overline{FI}\cong\overline{GH}$ (given), and $\overline{FH}\cong\overline{HF}$ (from step 1). By the Side - Side - Side (SSS) congruence criterion, $\triangle FGH\cong\triangle HIF$.

Answer:

$\overline{FH}\cong\overline{HF}$ (Reflexive property) is the missing statement for step 3, and then $\triangle FGH\cong\triangle HIF$ by SSS.