Question

statement reason
1 (overline{xy}congoverline{uv}) given
2 (angle wvxcongangle tuy) given
3 (angle tyucongangle vxw) given
4 (uy = xy+ux) additive property of length
5 (vx = uv+ux)
6 (uy = uv+ux) aas
additive property of angle measure
7 (vx = uy) additive property of length
all right angles are congruent
8 (\triangle tuycong\triangle wvx) alternate interior angles theorem
angles forming a linear pair sum to (180^{circ})
9 (overline{ty}congoverline{wx}) asa
corresponding angles theorem
cpctc
definition of angle bisector
definition of congruence
definition of equilateral triangle
definition of midpoint
given
properties of addition, subtraction, multiplication, and division
reflexive property of congruence
reflexive property of equality
sas
sss
substitution
transitive property of congruence
transitive property of equality
vertical angle theorem

Explanation:

Step1: Analyze the statement \( VX = UV+UX \)

This is about the length of a line segment. The additive property of length states that if a segment is composed of two adjacent sub - segments, then the length of the whole segment is the sum of the lengths of the sub - segments.

Answer:

Additive Property of Length