Question

statement reason
1 \\( \overline { x y } \cong \overline { u v } \\) given
2 \\( \overline { v w } \cong \overline { t u } \\) given
3 \\( \overline { t y } \cong \overline { w x } \\) given
4 \\( u y = x y + u x \\)
5 \\( v x = u v + u x \\) aas
6 \\( u y = u v + u x \\) additive property of length
7 \\( v x = u y \\) all right angles are congruent
8 \\( \triangle v w x \cong \triangle u t y \\) alternate interior angles theorem
asa
cpctc
definition of angle bisector
definition of congruence
definition of equilateral triangle
definition of midpoint
given
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 \( UY = XY + UX \)

This statement is about the relationship between the lengths of line - segments. The Additive Property of Length states that if a point \( X \) lies on a line - segment \( UY \), then \( UY=UX + XY \).

Answer:

Additive Property of Length