We have to prove UR = ST, given SU bisects RT and RT bisects SU.
1. TR bisects SU, SU bisects TR (Given)
2. UV = VS (V is the midpoint)
3. RV = VT (V is the midpoint)
4. mRVU = mSVT (Vertical angles)
5. RVU = VTS (by the postulate Side-Angle-Side, the two triangles are congruent)
6. RU = ST (if the triangles are congruent, all the corresponding sides have the same length)
Note: The SAS (Side-Angle-Side) postulate tells us that if two triangles have 2 sides with equal length and one angle with equal measure, the triangles are congruent and therefore have the same side lengths and same angles measures.
