Question

question 8 of 10
which property is illustrated by the following statement? if \\( \triangle z x y \cong \triangle f d e \\), and \\( \triangle f d e \cong \triangle c a b \\), then \\( \triangle z x y \cong \triangle c a b \\).
a. associative
b. symmetric
c. transitive
d. reflexive

Explanation:

The transitive property of congruence states that if \( \triangle A\cong\triangle B\) and \( \triangle B\cong\triangle C\), then \( \triangle A\cong\triangle C\). In the given statement, since \( \triangle ZXY\cong\triangle FDE\) and \( \triangle FDE\cong\triangle CAB\), we can conclude \( \triangle ZXY\cong\triangle CAB\) by the transitive property.
The associative property is related to the grouping of operations (e.g., in addition or multiplication \( (a + b)+c=a+(b + c)\)), which is not relevant here.
The symmetric property states that if \( \triangle A\cong\triangle B\), then \( \triangle B\cong\triangle A\).
The reflexive property states that \( \triangle A\cong\triangle A\).

Answer:

C. Transitive