Question

1. which property justifies the following statement? if ∠a ≅ ∠b and ∠b ≅ ∠c, then ∠a ≅ ∠c. reflexive property of congruence transitive property of congruence distributive property of congruence symmetric property of congruence

Explanation:

• The Reflexive Property of Congruence states that a figure is congruent to itself (e.g., $\angle a \cong \angle a$), which does not match the given statement.
• The Transitive Property of Congruence states that if $A \cong B$ and $B \cong C$, then $A \cong C$. This matches the structure of "If $\angle a \cong \angle b$ and $\angle b \cong \angle c$, then $\angle a \cong \angle c$".
• There is no Distributive Property of Congruence; the distributive property is related to operations like multiplication over addition, not congruence.
• The Symmetric Property of Congruence states that if $A \cong B$, then $B \cong A$, which is not the case here.

Answer:

B. Transitive Property of Congruence