Given the figure with $\overline{\mathrm{ER}}\cong \overline{\mathrm{FI}},\overline{\mathrm{EF}}\cong \overline{\mathrm{RI}},$ and $\angle \mathrm{FGI}$ and $\angle \mathrm{RUE}$ are right angles, prove that $\overline{\mathrm{FG}}\cong \overline{\mathrm{RU}}.$

Proof:

Statements	Reasons
1. $\overline{\mathrm{ER}}\cong \overline{\mathrm{FI}}$ $\overline{\mathrm{EF}}\cong \overline{\mathrm{RI}}$ $\angle \mathrm{FGI}$ and $\angle \mathrm{RUE}$ are right angles.	1. Given
2. $\overline{\mathrm{EI}}\cong \overline{\mathrm{EI}}$	2.
3. $\mathrm{\Delta EFI}\cong \mathrm{\Delta IRE}$	3.
4. $\angle \mathrm{FIE}\cong \angle \mathrm{REI}$	4.
5.	5. Definition of right triangles
6. $\mathrm{\Delta FGI}\cong \mathrm{\Delta RUE}$	6.
7. $\overline{\mathrm{FG}}\cong \overline{\mathrm{RU}}$	7. CPCTC