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Use the statement to answer the question.

If [tex] PQ = RS [/tex] and [tex] RS = 10 [/tex], then [tex] PQ = 10 [/tex].

If the statement is used in a two-column proof, what is the correct reason for the statement?

A. Multiplication Property of Equality
B. Reflexive Property of Equality
C. Transitive Property of Equality
D. Addition Property of Equality

Sagot :

GinnyAnsweridn
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
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