Question

1. which property or postulate justifies the statement below?

\if wx = yz, then wx + rs = yz + rs\
a. transitive property of equality
b. addition property of equality
c. segment addition postulate
d. substitution property of equality

Explanation:

The Addition Property of Equality states that if \( a = b \), then \( a + c = b + c \) for any real number \( c \). In the given statement, we have \( WX = YZ \), and then we add \( RS \) to both sides to get \( WX + RS = YZ + RS \), which matches the Addition Property of Equality. The Transitive Property (if \( a = b \) and \( b = c \), then \( a = c \)) doesn't apply here. The Segment Addition Postulate is about segment lengths forming a larger segment, not adding the same segment to equal segments. The Substitution Property involves replacing a quantity with an equal quantity, not adding to both sides.

Answer:

B. Addition Property of Equality