Question

if \\( \triangle a b c \cong \triangle c d a \\) then \\( \overline{a c} \\) (the diagonal of the quadrilateral) \\( \cong \overline{a c} \\) by which of the following properties?
option \\#1: division property of equality
option \\#2: reflexive property of equality
option \\#3: transitive property of equality
option \\#4: substitution property of equality
(1 point)
\\( \overline{a c} \cong \overline{a c} \\) by option \\#

Explanation:

Step1: Recall properties of equality

The reflexive property of equality states that \(a=a\) for any real number \(a\). In geometry, for a line - segment \(\overline{AC}\), \(\overline{AC}=\overline{AC}\) (or \(\overline{AC}\cong\overline{AC}\) when considering congruence of segments).

Step2: Analyze other properties

• Division Property of Equality: If \(a = b\) and \(c

eq0\), then \(\frac{a}{c}=\frac{b}{c}\). This is about division operation on equal quantities.

• Transitive Property of Equality: If \(a = b\) and \(b = c\), then \(a = c\). It is about a chain of equalities.
• Substitution Property of Equality: If \(a = b\), then \(a\) can be substituted for \(b\) in an expression.

Since \(\overline{AC}\cong\overline{AC}\) is of the form \(a = a\), it follows the reflexive property of equality.

Answer:

Option #2: Reflexive Property of Equality