In the figure, $\overline{\mathrm{IU}}\perp \overline{\mathrm{EL}},\overline{\mathrm{SC}}\perp \overline{\mathrm{EL}},\overline{\mathrm{IU}}\cong \overline{\mathrm{SC}},$ and $\overline{\mathrm{ED}}\cong \overline{\mathrm{DL}}.$ Prove that $\overline{\mathrm{EU}}\cong \overline{\mathrm{CL}}.$

Proof:

Statements	Reasons
1. $\overline{\mathrm{IU}}\perp \overline{\mathrm{EL}}$ $\overline{\mathrm{SC}}\perp \overline{\mathrm{EL}}$ $\overline{\mathrm{IU}}\cong \overline{\mathrm{SC}}$ $\overline{\mathrm{ED}}\cong \overline{\mathrm{DL}}$	1. Given
2. $\angle E\cong \angle L$	2.
3. $\angle \mathrm{IUE}$ and $\angle \mathrm{SCL}$ are right angles.	3.
4.	4. Definition of right triangles
5. $\mathrm{\Delta IUE}\cong \mathrm{\Delta SCL}$	5.
6. $\overline{\mathrm{EU}}\cong \overline{\mathrm{CL}}$	6.