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Answer :
Sure! Let's understand what the symmetric property of congruence is and how it applies to the provided options.
The symmetric property of congruence is a fundamental property in geometry. It states that if one figure is congruent to another, then the second figure is congruent to the first. In other words, if [tex]\( A \cong B \)[/tex], then [tex]\( B \cong A \)[/tex].
Now let's analyze each option:
A. [tex]\( AKLM \cong AKLM \)[/tex] - This is a tautology, meaning a shape is congruent to itself. It doesn't demonstrate the symmetric property.
B. If [tex]\( AKLM \cong APQR \)[/tex], then [tex]\( APQR = ASTU \)[/tex] - This describes a different concept other than symmetry, possibly grouping toward transitive property if further reasoning is allowed, which involves a third element.
C. If [tex]\( AKLM \cong APQR \)[/tex], then [tex]\( APQR \cong AKLM \)[/tex] - This is precisely the definition of the symmetric property of congruence. It states that the congruence relationship works both ways between two figures.
D. If [tex]\( AKLM \cong APQR \)[/tex], and [tex]\( APQR \cong ASTU \)[/tex], then [tex]\( AKLM \cong ASTU \)[/tex] - This is an example of the transitive property, not the symmetric property. The transitive property involves a third element to link congruence.
Therefore, the statement that exemplifies the symmetric property of congruence is option C: "If [tex]\( AKLM \cong APQR \)[/tex], then [tex]\( APQR \cong AKLM \)[/tex]."
The symmetric property of congruence is a fundamental property in geometry. It states that if one figure is congruent to another, then the second figure is congruent to the first. In other words, if [tex]\( A \cong B \)[/tex], then [tex]\( B \cong A \)[/tex].
Now let's analyze each option:
A. [tex]\( AKLM \cong AKLM \)[/tex] - This is a tautology, meaning a shape is congruent to itself. It doesn't demonstrate the symmetric property.
B. If [tex]\( AKLM \cong APQR \)[/tex], then [tex]\( APQR = ASTU \)[/tex] - This describes a different concept other than symmetry, possibly grouping toward transitive property if further reasoning is allowed, which involves a third element.
C. If [tex]\( AKLM \cong APQR \)[/tex], then [tex]\( APQR \cong AKLM \)[/tex] - This is precisely the definition of the symmetric property of congruence. It states that the congruence relationship works both ways between two figures.
D. If [tex]\( AKLM \cong APQR \)[/tex], and [tex]\( APQR \cong ASTU \)[/tex], then [tex]\( AKLM \cong ASTU \)[/tex] - This is an example of the transitive property, not the symmetric property. The transitive property involves a third element to link congruence.
Therefore, the statement that exemplifies the symmetric property of congruence is option C: "If [tex]\( AKLM \cong APQR \)[/tex], then [tex]\( APQR \cong AKLM \)[/tex]."
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