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Which statement is an example of the symmetric property of congruence?



A. If \( \angle KLM \cong \angle PQR \), then \( \angle PQR \cong \angle KLM \).

B. If \( \angle KLM \cong \angle PQR \), then \( \angle PQR \cong \angle STU \).

C. If \( \angle KLM \cong \angle PQR \) and \( \angle PQR \cong \angle STU \), then \( \angle KLM \cong \angle STU \).

D. \( \angle KLM \cong \angle KLM \)

Answer :

The symmetric property of congruence tells us that if one figure is congruent to another, then the second figure is congruent to the first. In mathematical terms, if

$$ A \cong B, $$

then it must also be true that

$$ B \cong A. $$

Now, let’s analyze the options:

1. **Option A:** "If $AKLM \cong APQR$, then $APQR = AKLM$."
This option directly states that if one figure is congruent to another, then the order can be reversed (i.e., the second is congruent to the first). This is exactly what the symmetric property of congruence expresses.

2. **Options B, C, and D:**
- Option B introduces a different figure ($ASTU$) which is not part of the given congruence relation, so it does not demonstrate the symmetric property.
- Option C involves a third figure, showing a comparison between two figures that are each congruent to a common figure, which instead illustrates the transitive property of congruence.
- Option D simply repeats the congruence of a figure to itself and does not demonstrate the proper use of the symmetric property.

Thus, the correct answer is:

$$ \textbf{Option A} $$

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Rewritten by : Barada