Question

given: \\( \angle abc \cong \angle efg \\) prove: \\( m \angle abc = m \angle def \\)

Explanation:

Step1: Definition of congruent angles

Congruent angles have equal measures. If \(\angle ABC\cong\angle EFG\), then \(m\angle ABC = m\angle EFG\) by the definition of congruent angles.

Step2: Transitive property (assuming \(\angle EFG\cong\angle DEF\) which is missing in the problem statement but needed for the conclusion \(m\angle ABC=m\angle DEF\))

If \(m\angle ABC = m\angle EFG\) and \(m\angle EFG=m\angle DEF\) (by congruence of \(\angle EFG\) and \(\angle DEF\)), then by the transitive property of equality \(m\angle ABC = m\angle DEF\).

Answer:

Transitive property of equality (assuming \(\angle EFG\cong\angle DEF\) as an implicit given or derived step)