Question

statement reason
1 sv bisects ∠tvx given
2 sv bisects ∠usw given
3 ∠wvx ≅ ∠tvu vertical angle theorem
4 ∠svx ≅ ∠svt definition of angle bisector
5 ∠vsw ≅ ∠usv definition of angle bisector
6 m∠svw = m∠svx + m∠wvx
7 m∠svu = m∠svt + m∠tvu additive property of angle measure
8 m∠svw = m∠svt + m∠tvu substitution
9 m∠svu = m∠svw transitive property of equality
10 sv ≅ sv
11 △svw ≅ △svu asa
12 su ≅ sw cpctc

Explanation:

Step1: Recall the Angle - Addition Postulate

The Angle - Addition Postulate states that if a point \(B\) lies in the interior of \(\angle AOC\), then \(m\angle AOC=m\angle AOB + m\angle BOC\).
In the case of \(\angle SVW\), if we consider \(\angle SVX\) and \(\angle WVX\) as two non - overlapping angles that form \(\angle SVW\) (i.e., the vertex \(V\) and the rays \(VS\), \(VX\), \(VW\) such that \(VX\) is between \(VS\) and \(VW\)), then by the Angle - Addition Postulate:
\(m\angle SVW=m\angle SVX + m\angle WVX\)

Answer:

Angle - Addition Postulate