Question

question 1
10 pts
g.gsr.3.4 (lc)
which answer choice best describes the substitution property of equality?
an angle or line segment is always congruent to itself.
we can subtract the same value from both sides of an equation.
if a = b, then that is always a true statement and cannot be transformed.
if a = b, then a and b can be used interchangeably in any statement.

Explanation:

1. Analyze the first option: This describes the Reflexive Property (e.g., \( \angle A \cong \angle A \) or \( \overline{AB} \cong \overline{AB} \)), not Substitution.
2. Analyze the second option: This is the Subtraction Property of Equality (if \( a = b \), then \( a - c = b - c \)), not Substitution.
3. Analyze the third option: This is incorrect. Equalities can be transformed (e.g., using properties of equality), and the Substitution Property allows replacing \( a \) with \( b \) (or vice versa) in expressions.
4. Analyze the fourth option: The Substitution Property of Equality states that if \( a = b \), then \( a \) can be substituted for \( b \) (and \( b \) for \( a \)) in any mathematical statement, which matches this description.

Answer:

D. If \( a = b \), then \( a \) and \( b \) can be used interchangeably in any statement.