To understand which property justifies the statement "If [tex]\(a = b\)[/tex] and [tex]\(b = c\)[/tex], then [tex]\(a = c\)[/tex]," we need to consider the different properties of equality in mathematics.
1. Addition Property: This property states that if [tex]\(a = b\)[/tex], then [tex]\(a + c = b + c\)[/tex] for any [tex]\(c\)[/tex]. This property is related to the addition of equal quantities.
2. Reflexive Property: This property states that any quantity is equal to itself, i.e., [tex]\(a = a\)[/tex]. It is fundamental but does not involve multiple quantities or the chaining of equalities.
3. Subtraction Property: This property states that if [tex]\(a = b\)[/tex], then [tex]\(a - c = b - c\)[/tex] for any [tex]\(c\)[/tex]. This property is similar to the addition property but involves subtraction.
4. Transitive Property: This property states that if [tex]\(a = b\)[/tex] and [tex]\(b = c\)[/tex], then [tex]\(a = c\)[/tex]. It involves three quantities and shows how the equality can be transferred across them.
The given statement "If [tex]\(a = b\)[/tex] and [tex]\(b = c\)[/tex], then [tex]\(a = c\)[/tex]" is directly described by the Transitive Property. This property allows us to conclude that two things are equal if they are both equal to a third thing.
Given the options, the property that would justify the statement is:
- Transitive Property
Therefore, the correct answer is the 4th option: Transitive Property.
