Question

1. which property or postulate justifies the statement below?

\if ( mangle 1 + mangle 3 = mangle 4 ), and ( mangle 3 = mangle 2 ),
then ( mangle 1 + mangle 2 = mangle 4 ).\
a. substitution property of equality
b. angle addition postulate
c. addition property of equality
d. transitive property of equality

Explanation:

The Substitution Property of Equality states that if two quantities are equal, one can be substituted for the other in an equation. Here, since \( m\angle3 = m\angle2 \), we substitute \( m\angle2 \) for \( m\angle3 \) in the equation \( m\angle1 + m\angle3 = m\angle4 \), resulting in \( m\angle1 + m\angle2 = m\angle4 \). The Angle Addition Postulate deals with adding angles to form a larger angle, the Addition Property of Equality involves adding the same quantity to both sides of an equation, and the Transitive Property involves if \( a = b \) and \( b = c \), then \( a = c \), which doesn't apply here. So the correct property is the Substitution Property of Equality.

Answer:

A. Substitution Property of Equality