Question

statement
1 (overleftrightarrow{sv}) bisects (angle tvx) given
2 (overleftrightarrow{sv}) bisects (angle usw) given
3 (angle wvxcongangle tvu) vertical angle theorem
4 (angle svxcongangle svt) definition of angle bisector
5 (angle vswcongangle usv) definition of angle bisector
6 (mangle svw = mangle svx + mangle wvx) additive property of length
7 (mangle svu = mangle svt + mangle tvu) additive property of angle measure
8 (mangle svw = mangle svt + mangle tvu) substitution
9 (mangle svu = mangle svw) transitive property of equality
10 (overline{sv}congoverline{sv})
11 (\triangle svwcong\triangle svu) asa
12 (overline{su}congoverline{sw}) cpctc

Explanation:

Step1: Analyze the reason for statement 6

The formula \(m\angle SVW=m\angle SVX + m\angle WVX\) is about the measure of an angle being the sum of two non - overlapping adjacent angles. This is based on the Additive Property of Angle Measure, not the Additive Property of Length.

Answer:

The correct reason for statement 6 should be "Additive Property of Angle Measure".