Question

∠rtv ≅ ∠rus, \overline{ru} ≅ \overline{rt}, and ∠srt ≅ ∠urv. complete the proof that \overline{tv} ≅ \overline{su}.
1 ∠rtv ≅ ∠rus given
2 \overline{ru} ≅ \overline{rt} given
3 ∠srt ≅ ∠urv given
4 m∠trv = m∠tru + m∠urv additive property of angle measure
5 m∠sru = m∠srt + m∠tru
6 m∠trv = m∠tru + m∠srt
7 m∠sru = m∠trv transitive property of equality
8 △rtv ≅ △rus asa
9 \overline{tv} ≅ \overline{su} cpctc

Explanation:

Step1: Reason for statement 5

Additive Property of Angle Measure.

Step2: Reason for statement 6

Substitution Property of Equality (since \( \angle SRT\cong\angle URV\), so \(m\angle URV = m\angle SRT\) and substitute into \(m\angle TRV=m\angle TRU + m\angle URV\)).

Answer:

1. Additive Property of Angle Measure; 6. Substitution Property of Equality.