Question

question 7 of 10
which statement is an example of the symmetric property of congruence?

a. if $\triangle klm \cong \triangle pqr$, and $\triangle pqr \cong \triangle stu$, then $\triangle klm \cong \triangle stu$.

b. $\triangle klm \cong \triangle klm$

c. if $\triangle klm \cong \triangle pqr$, then $\triangle pqr \cong \triangle stu$.

d. if $\triangle klm \cong \triangle pqr$, then $\triangle pqr \cong \triangle klm$.

Explanation:

The symmetric property of congruence states that if one figure is congruent to another, then the second figure is congruent to the first. Let's analyze each option:

• Option A: This is the transitive property of congruence (if \( A\cong B \) and \( B\cong C \), then \( A\cong C \)), not symmetric.
• Option B: This is the reflexive property of congruence (a figure is congruent to itself), not symmetric.
• Option C: The conclusion does not follow the symmetric property as it introduces a new triangle (\( \triangle STU \)) not related by the symmetric property to \( \triangle KLM \) or \( \triangle PQR \) in the given premise.
• Option D: If \( \triangle KLM\cong\triangle PQR \), then by the symmetric property, \( \triangle PQR\cong\triangle KLM \), which matches the definition of the symmetric property of congruence.

Answer:

D. If \( \triangle KLM \cong \triangle PQR \), then \( \triangle PQR \cong \triangle KLM \)