Answer :
Sure, let's break down the choices and identify which one exemplifies the symmetric property of congruence.
The symmetric property of congruence states that if one figure is congruent to another, then the second figure is congruent to the first. In other words, if A is congruent to B, then B is congruent to A.
Let's analyze each statement:
Choice A: If AKLMA PQR, then APQRAKLM.
- Here, if figure AKLM is congruent to PQR, it asserts that PQR is also congruent to AKLM. This matches the symmetric property of congruence perfectly.
Choice B: If AKLMA PQR, then APQR = ASTU.
- This choice does not reflect the symmetric property. Instead, it introduces another relationship between APQR and ASTU, which is irrelevant to the symmetric property.
Choice C: If AKLMA PQR, and APQR = ASTU, then AKLM ASTU.
- This choice suggests a transitive relationship rather than a symmetric one. The transitive property states that if A is congruent to B and B is congruent to C, then A is congruent to C.
Choice D: AKLMAKLM.
- This simply restates that a figure is congruent to itself, which is not relevant to the symmetric property but rather the reflexive property.
Based on this detailed analysis:
The correct answer is Choice A: If AKLMA PQR, then APQRAKLM.
The symmetric property of congruence states that if one figure is congruent to another, then the second figure is congruent to the first. In other words, if A is congruent to B, then B is congruent to A.
Let's analyze each statement:
Choice A: If AKLMA PQR, then APQRAKLM.
- Here, if figure AKLM is congruent to PQR, it asserts that PQR is also congruent to AKLM. This matches the symmetric property of congruence perfectly.
Choice B: If AKLMA PQR, then APQR = ASTU.
- This choice does not reflect the symmetric property. Instead, it introduces another relationship between APQR and ASTU, which is irrelevant to the symmetric property.
Choice C: If AKLMA PQR, and APQR = ASTU, then AKLM ASTU.
- This choice suggests a transitive relationship rather than a symmetric one. The transitive property states that if A is congruent to B and B is congruent to C, then A is congruent to C.
Choice D: AKLMAKLM.
- This simply restates that a figure is congruent to itself, which is not relevant to the symmetric property but rather the reflexive property.
Based on this detailed analysis:
The correct answer is Choice A: If AKLMA PQR, then APQRAKLM.
