Question

1. consider the following argument. given: ( mangle abc = mangle def ) and ( mangle def = 75^circ ) conclusion: ( mangle abc = 75^circ ) which of the following properties does this illustrate? the multiplication property of equality. a the reflexive property of equality. b the transitive property of equality. c the addition property of equality. d the symmetric property of equality. e

Explanation:

The transitive property of equality states that if \( a = b \) and \( b = c \), then \( a = c \). Here, we have \( m\angle ABC = m\angle DEF \) (so \( a = b \)) and \( m\angle DEF = 75^\circ \) (so \( b = c \)), leading to \( m\angle ABC = 75^\circ \) (so \( a = c \)), which matches the transitive property. The other properties don't apply: multiplication/addition properties involve operations on both sides, reflexive is \( a = a \), symmetric is if \( a = b \) then \( b = a \).

Answer:

C. The transitive property of equality.