Question

1 ∠rws ≅ ∠tvu given
2 ∠srw ≅ ∠tuv given
3 \overline{vw} ≅ \overline{st} given
4 sw = vw + sv
5 tv = st + sv
6 sw = st + sv
7 tv = sw transitive property of equality
8 △rsw ≅ △utv aas

Explanation:

Step1: Segment Addition Postulate

The Segment Addition Postulate states that if \(A\), \(B\), and \(C\) are collinear points and \(B\) is between \(A\) and \(C\), then \(AB + BC=AC\). For segment \(SW\), since \(V\) is between \(S\) and \(W\), \(SW = VW+SV\).

Step2: Segment Addition Postulate

For segment \(TV\), since \(S\) is between \(T\) and \(V\), \(TV = ST + SV\) by the Segment Addition Postulate.

Step3: Substitution Property of Equality

Given that \(VW\cong ST\) (i.e., \(VW = ST\)), substitute \(VW\) with \(ST\) in the equation \(SW = VW+SV\). So, \(SW=ST + SV\) by the Substitution Property of Equality.

Answer:

1. Segment Addition Postulate; 5. Segment Addition Postulate; 6. Substitution Property of Equality.