To solve the question, consider the given statements:
1. [tex]\( PQ = RS \)[/tex]
2. [tex]\( RS = 10 \)[/tex]
We need to find the value of [tex]\( PQ \)[/tex]. We can use these two statements in the proof.
To begin, let's apply the properties of equality:
1. From the first statement given, we know that [tex]\( PQ = RS \)[/tex].
2. From the second statement given, we know that [tex]\( RS = 10 \)[/tex].
The key principle here is the Transitive Property of Equality. The Transitive Property of Equality states that if [tex]\( a = b \)[/tex] and [tex]\( b = c \)[/tex], then [tex]\( a = c \)[/tex]. In this case:
- We have [tex]\( PQ = RS \)[/tex] (where [tex]\( PQ \)[/tex] and [tex]\( RS \)[/tex] are the expressions in our given equations).
- We also have [tex]\( RS = 10 \)[/tex] (where [tex]\( RS \)[/tex] and 10 are equal).
By applying the Transitive Property of Equality:
Since [tex]\( PQ = RS \)[/tex] and [tex]\( RS = 10 \)[/tex], we can conclude that [tex]\( PQ = 10 \)[/tex].
Thus, the correct reason for the statement [tex]\( PQ = 10 \)[/tex] is the:
Transitive Property of Equality
Therefore, the correct answer is:
Transitive Property of Equality
