Question

from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement. given: (\frac{1}{2}mangle abc = \frac{1}{2}mangle nmv) prove: (mangle abc = mangle nmv)

Explanation:

Step1: Recall the property

The Multiplication Property of Equality states that if \( a = b \), then \( c \cdot a = c \cdot b \) for any real number \( c \), and also if \( \frac{1}{c} \cdot a=\frac{1}{c} \cdot b \) (where \( c
eq0 \)), then multiplying both sides by \( c \) gives \( a = b \).

Step2: Apply the property

Given \( \frac{1}{2}m\angle ABC=\frac{1}{2}m\angle NMV \), we multiply both sides of the equation by \( 2 \) (which is the reciprocal of \( \frac{1}{2} \) and a non - zero real number).
Using the formula for the Multiplication Property of Equality, if we let \( a = m\angle ABC \), \( b = m\angle NMV \), and \( c = 2 \), and our initial equation is \( \frac{1}{2}a=\frac{1}{2}b \), then multiplying both sides by \( 2 \) gives \( 2\times\frac{1}{2}a=2\times\frac{1}{2}b \), which simplifies to \( a = b \) or \( m\angle ABC = m\angle NMV \).

Answer:

Multiplication Property of Equality