Question

what is the missing justification?
\\( \angle a \cong \angle b, \angle c \cong \angle b \\) given
\\( \angle b \cong \angle c \\) symmetric prop
\\( \angle a \cong \angle c \\) ?
\\( m \angle a = m \angle c \\) def of \\( \cong \angle s \\)
o transitive property
o reflexive property
o symmetric property
o substitution property

Explanation:

Step1: Recall the transitive property

If \(a = b\) and \(b = c\), then \(a = c\).

Step2: Apply to angles

Here, \(\angle A\cong\angle B\) (so \(m\angle A = m\angle B\)) and \(\angle C\cong\angle B\) (so \(m\angle C=m\angle B\)). By transitive property of equality (since congruent angles have equal measures), if \(m\angle A = m\angle B\) and \(m\angle C=m\angle B\), then \(m\angle A=m\angle C\) which implies \(\angle A\cong\angle C\). The transitive property for congruence of angles states that if \(\angle X\cong\angle Y\) and \(\angle Y\cong\angle Z\), then \(\angle X\cong\angle Z\).

Answer:

transitive property