To determine which property of equality is being described, let's carefully consider the statement provided:
The Property of Equality states that for any numbers [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex], if [tex]\(a = b\)[/tex] and [tex]\(b = c\)[/tex], then [tex]\(a = c\)[/tex].
Let's examine the options:
1. Reflexive Property: This property states that any number is equal to itself. Formally, for any number [tex]\(a\)[/tex], [tex]\(a = a\)[/tex]. Clearly, this property does not deal with the relationships between three different numbers [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex].
2. Associative Property: This property typically pertains to the operations of addition and multiplication and states that the way in which numbers are grouped does not affect the result. For example, [tex]\((a + b) + c = a + (b + c)\)[/tex] and [tex]\((a \cdot b) \cdot c = a \cdot (b \cdot c)\)[/tex]. This property does not describe equality between numbers.
3. Transitive Property: This property specifically addresses the relationship among three numbers with respect to equality. It states that if [tex]\(a = b\)[/tex] and [tex]\(b = c\)[/tex], then [tex]\(a = c\)[/tex]. This is exactly what the statement in the question describes.
Thus, the correct answer is:
Transitive
The Transitive Property of Equality correctly describes the statement: for any numbers [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex], if [tex]\(a = b\)[/tex] and [tex]\(b = c\)[/tex], then [tex]\(a = c\)[/tex].
