Question

∠a ≅ ∠b, ∠c ≅ ∠b given
∠b ≅ ∠c symmetric prop.
∠a ≅ ∠c ?
m∠a = m∠c def. of ≅ ∠s
what is the missing justification?
○ transitive property
○ reflexive property
○ symmetric property
○ substitution property

Explanation:

We know that \( \angle A \cong \angle B \) and \( \angle B \cong \angle C \) (after using the symmetric property on \( \angle C \cong \angle B \) to get \( \angle B \cong \angle C \)). The transitive property of congruence states that if \( \angle X \cong \angle Y \) and \( \angle Y \cong \angle Z \), then \( \angle X \cong \angle Z \). Here, \( X = A \), \( Y = B \), \( Z = C \), so using the transitive property, we can conclude \( \angle A \cong \angle C \). The reflexive property is about a quantity being congruent to itself, the symmetric property is about reversing the congruence (like if \( \angle X \cong \angle Y \), then \( \angle Y \cong \angle X \)), and substitution is about replacing a quantity with an equal one, which doesn't apply here. So the missing justification is the transitive property.

Answer:

A. transitive property