Reasons:
a. SAS Congruence Postulate
b. Given
c. Definition of perpendicular segments
d. Any two right angles are congruent.

Proof:

Statements	Reasons
1. $\overline{\mathrm{VW}}\cong \overline{\mathrm{YZ}}$ $\overline{\mathrm{VW}}\perp \overline{\mathrm{WX}}$ $\overline{\mathrm{YZ}}\perp \overline{\mathrm{ZX}}$	1. Given
2. $\angle \mathrm{VWX}$ is a right angle. $\angle \mathrm{YZX}$ is a right angle.	2.
3. $\angle \mathrm{VWX}\cong \angle \mathrm{YZX}$	3.
4. $\overline{\mathrm{WX}}\cong \overline{\mathrm{ZX}}$	4.
5. $\mathrm{\Delta VWX}\cong \mathrm{\Delta YZX}$	5.

Reasons:
a. SAA Congruence Postulate
b. Alternate Interior Angles Theorem
c. Vertical Angles Theorem
d. Given

Proof:

Statements	Reasons
1. $\overline{\mathrm{MA}}\left|\right|\overline{\mathrm{IE}}$ $\overline{\mathrm{MA}}\cong \overline{\mathrm{IE}}$	1.
2. $\angle \mathrm{MRA}\cong \angle \mathrm{IRE}$	2.
3. $\angle M\cong \angle E$	3.
4. $\mathrm{\Delta MAR}\cong \mathrm{\Delta EIR}$	4.