Question

which of the following properties is the reason for the statement: \\( \overline { a c } \cong \overline { a c } \\)

reflexive property
symmetric property
transitive property
distributive property

Explanation:

The Reflexive Property states that any geometric figure (like a line segment) is congruent to itself. Here, $\overline{AC}$ is congruent to $\overline{AC}$, which directly follows the Reflexive Property. The Symmetric Property is about if \(a = b\) then \(b=a\) (for congruence, if \(A\cong B\) then \(B\cong A\)). The Transitive Property is if \(a = b\) and \(b = c\) then \(a = c\) (for congruence, if \(A\cong B\) and \(B\cong C\) then \(A\cong C\)). The Distributive Property is \(a(b + c)=ab+ac\) (an algebraic property, not related to congruence of geometric figures).

Answer:

Reflexive Property