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Answer :
To solve this question, we need to identify which statement is an example of the symmetric property of congruence.
The symmetric property of congruence states that if one geometric figure is congruent to another, then the second figure is also congruent to the first. In other words, if [tex]\( A \cong B \)[/tex], then [tex]\( B \cong A \)[/tex].
Let's examine each option:
A. [tex]\( \triangle KLM \cong \triangle KLM \)[/tex] - This statement shows reflexive property (a figure is congruent to itself), not symmetric.
B. If [tex]\( \triangle KLM \cong \triangle PQR \)[/tex], then [tex]\( \triangle PQR = \triangle STU \)[/tex]. - This statement introduces a new figure without stating that [tex]\( \triangle KLM \)[/tex] is congruent to [tex]\( \triangle STU \)[/tex], so it doesn't demonstrate symmetry.
C. If [tex]\( \triangle KLM \cong \triangle POR \)[/tex], then [tex]\( \triangle POR \cong \triangle KLM \)[/tex]. - This fits the symmetric property perfectly because it shows if [tex]\( \triangle KLM \cong \triangle POR \)[/tex], then [tex]\( \triangle POR \cong \triangle KLM \)[/tex].
D. If [tex]\( \triangle KLM \cong \triangle PQR \)[/tex], and [tex]\( \triangle PORE \cong \triangle STU \)[/tex], then [tex]\( \triangle KLM = \triangle STU \)[/tex]. - This statement involves a transitive property, not symmetric.
The correct answer that demonstrates the symmetric property of congruence is option C: If [tex]\( \triangle KLM \cong \triangle POR \)[/tex], then [tex]\( \triangle POR \cong \triangle KLM \)[/tex].
The symmetric property of congruence states that if one geometric figure is congruent to another, then the second figure is also congruent to the first. In other words, if [tex]\( A \cong B \)[/tex], then [tex]\( B \cong A \)[/tex].
Let's examine each option:
A. [tex]\( \triangle KLM \cong \triangle KLM \)[/tex] - This statement shows reflexive property (a figure is congruent to itself), not symmetric.
B. If [tex]\( \triangle KLM \cong \triangle PQR \)[/tex], then [tex]\( \triangle PQR = \triangle STU \)[/tex]. - This statement introduces a new figure without stating that [tex]\( \triangle KLM \)[/tex] is congruent to [tex]\( \triangle STU \)[/tex], so it doesn't demonstrate symmetry.
C. If [tex]\( \triangle KLM \cong \triangle POR \)[/tex], then [tex]\( \triangle POR \cong \triangle KLM \)[/tex]. - This fits the symmetric property perfectly because it shows if [tex]\( \triangle KLM \cong \triangle POR \)[/tex], then [tex]\( \triangle POR \cong \triangle KLM \)[/tex].
D. If [tex]\( \triangle KLM \cong \triangle PQR \)[/tex], and [tex]\( \triangle PORE \cong \triangle STU \)[/tex], then [tex]\( \triangle KLM = \triangle STU \)[/tex]. - This statement involves a transitive property, not symmetric.
The correct answer that demonstrates the symmetric property of congruence is option C: If [tex]\( \triangle KLM \cong \triangle POR \)[/tex], then [tex]\( \triangle POR \cong \triangle KLM \)[/tex].
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