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 \(a = a\). Here, it's about two equal angles swapping positions, not \(a=a\), so not reflexive.
• Substitution property: Replaces a quantity with its equal in an expression. This is just swapping the order of equality, not substitution.
• Symmetric property: If \(a = b\), then \(b=a\). Here, \(m\angle ABC=m\angle CBD\) and then \(m\angle CBD = m\angle ABC\) which fits \(a = b\Rightarrow b=a\).
• Transitive property: If \(a = b\) and \(b = c\), then \(a=c\). There are only two angles here, not three, so not transitive.

Answer:

symmetric property