Question

which property of congruency states if $\triangle rst \cong \triangle r_1s_1t_1$ then $\triangle r_1s_1t_1 \cong \triangle rst$?
\bigcirc transitive property of congruence
\bigcirc distributive property of congruence
\bigcirc symmetric property of congruence
\bigcirc reflexive property of congruence

Explanation:

To determine the correct property, we analyze each option:

• Transitive Property: If \( A \cong B \) and \( B \cong C \), then \( A \cong C \). This doesn't match the given scenario.
• Distributive Property: This is a property of operations (like multiplication over addition), not congruence.
• Symmetric Property of Congruence: If \( A \cong B \), then \( B \cong A \). In the problem, if \( \triangle RST \cong \triangle R_1S_1T_1 \), then \( \triangle R_1S_1T_1 \cong \triangle RST \), which fits the symmetric property.
• Reflexive Property: Every figure is congruent to itself (\( A \cong A \)), which is not the case here.

Answer:

C. Symmetric Property of Congruence