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

A. [tex] \angle KLM = \angle KLM [/tex]

B. If [tex] \angle KLM = \angle PQR [/tex], then [tex] \angle PQR = \angle KLM [/tex].

C. If [tex] \angle KLM = \angle PQR [/tex], then [tex] \angle PQR = \angle STU [/tex].

D. If [tex] \angle KLM = \angle PQR [/tex], and [tex] \angle PQR = \angle STU [/tex], then [tex] \angle KLM = \angle STU [/tex].

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 we have

[tex]$$
A = B,
$$[/tex]

then it must also be true that

[tex]$$
B = A.
$$[/tex]

Let's analyze the given options:

1. Option A does not provide a clear statement.
2. Option B states: "If [tex]$AKLMAPQR$[/tex], then [tex]$APQR = AKLM$[/tex]." This directly mirrors the idea that if one figure (in this case, [tex]$AKLM$[/tex]) is congruent to another ([tex]$APQR$[/tex]), then the second is congruent to the first. This is an example of the symmetric property.
3. Option C introduces a different figure ([tex]$ASTU$[/tex]) in the conclusion, which does not match the symmetry requirement.
4. Option D combines multiple congruencies and uses the transitive property rather than simply reflecting the symmetric property.

Thus, the correct answer that exemplifies the symmetric property of congruence is option 2.

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