We will have the following:
From the 2nd point on:
*RU congruent with VS.
*2. Definition of congruent segments.
*VS = RS + SU
*3. Segment addition postulate.
*RU = RS + SU, VS = VU + SU
*4. Substitution property of equality,
*RS = VU.
*5. Transitive property of equality,
*RU = VS
*6. Deffinition of congruent segments.
*Triangles PUR and QSV are congruent.
*7. ASA congruence therorem.
*
*8. Corresponding parts of congruent triangles are congruent.
*m*11. Substitution property of equality.
*m*12. Transitive property of equality.
**13. Definition of congruent angles.
*Triangles PUX & QSY are congruent.
*ASA congruence theorem.
