Answer: The statement that exemplifies the symmetric property of congruence is B. If AKLM APQR, then APQR = KLM.
Explanation:
The symmetric property of congruence states that if two geometric figures are congruent, then their corresponding parts are also congruent.
Looking at the given options:
A. If KLM APQR, then APQR = ASTU.
This statement does not demonstrate the symmetric property of congruence because it only states the congruence of KLM and APQR, without considering the corresponding parts.
B. If AKLM APQR, then APQR = KLM.
This statement demonstrates the symmetric property of congruence. It states that if AKLM and APQR are congruent, then their corresponding parts, APQR and KLM, are also congruent.
C. AKLM AKLM
This statement does not demonstrate the symmetric property of congruence as it is simply stating that AKLM is congruent to itself, which is a reflexive property.
D. If AKLM APQR, and APQR = ASTU, then KLM = ASTU.
This statement does not demonstrate the symmetric property of congruence because it relates the congruence of AKLM and APQR to the congruence of APQR and ASTU, without directly comparing the corresponding parts of AKLM and ASTU.
Therefore, the statement that exemplifies the symmetric property of congruence is B. If AKLM APQR, then APQR = KLM. This statement acknowledges that if two figures are congruent, then their corresponding parts are also congruent.