Question

question 14 module 3 test-logic and line relationships
4 $overline{xy}congoverline{yz}$ and $overline{yz}congoverline{zw}$ 4 ______

1. $xy = yz$ and $yz = zw$ 5. definition of congruent
2. $xy=zw$ 6. transitive property

7 $overline{xy}congoverline{zw}$ 7. definition of congruent segments
a) midpoint theorem
b) congruent segments
c) definition of congruence
d) segment addition property

Explanation:

The statement $\overline{XY}\cong\overline{YZ}$ and $\overline{YZ}\cong\overline{ZW}$ is based on the concept that congruent segments have equal lengths. The transition from congruence notation ($\cong$) to equality of lengths ($=$) in step 5 is by the definition of congruent segments. So, the reason for step 4 is the definition of congruence which links the geometric congruence relation to the algebraic equality of lengths.

Answer:

C. Definition of Congruence