Question

which property is shown? if ( mangle abc = mangle cbd ), then ( mangle cbd = mangle abc ) reflexive property substitution property symmetric property transitive property

Explanation:

• Reflexive property: States \(a = a\). This is not the case here as we have \(m\angle ABC=m\angle CBD\) and then \(m\angle CBD = m\angle ABC\).
• Substitution property: If \(a = b\), then \(a\) can be substituted for \(b\) in an expression. This is not relevant to the given statement of swapping the order of equality.
• Symmetric property: If \(a=b\), then \(b = a\). Here, if \(m\angle ABC=m\angle CBD\), then \(m\angle CBD=m\angle ABC\) follows the form \(a = b\Rightarrow b=a\).
• Transitive property: If \(a=b\) and \(b = c\), then \(a=c\). This is not the situation described.

Answer:

symmetric property