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Answer :
To solve this question, we need to identify the example of the transitive property of congruence. The transitive property in mathematics states that if one thing is equal (or congruent) to a second, and the second is equal (or congruent) to a third, then the first is also equal (or congruent) to the third.
Let's evaluate each statement to see which one best exemplifies this property:
A. If AKLM ≅ APQR, then APQR ≅ AKLM.
- This statement shows symmetry, not transitivity. Symmetry means if one thing is congruent to another, you can reverse the order and they are still congruent.
B. AKLM ≅ AKLM.
- This statement illustrates the reflexive property, which means everything is congruent to itself.
C. If AKLM ≅ APQR, then APQR ≅ ASTU.
- This statement doesn't provide adequate information for transitivity because it skips a step. It doesn't tell you how APQR is related to ASTU in terms of the first figure.
D. If AKLM ≅ APQR and APQR ≅ ASTU, then AKLM ≅ ASTU.
- This statement is a prime example of the transitive property: If AKLM is congruent to APQR and APQR is congruent to ASTU, then AKLM is congruent to ASTU.
Based on the explanation, statement D is the example of the transitive property of congruence. Therefore, the correct choice is option D.
Let's evaluate each statement to see which one best exemplifies this property:
A. If AKLM ≅ APQR, then APQR ≅ AKLM.
- This statement shows symmetry, not transitivity. Symmetry means if one thing is congruent to another, you can reverse the order and they are still congruent.
B. AKLM ≅ AKLM.
- This statement illustrates the reflexive property, which means everything is congruent to itself.
C. If AKLM ≅ APQR, then APQR ≅ ASTU.
- This statement doesn't provide adequate information for transitivity because it skips a step. It doesn't tell you how APQR is related to ASTU in terms of the first figure.
D. If AKLM ≅ APQR and APQR ≅ ASTU, then AKLM ≅ ASTU.
- This statement is a prime example of the transitive property: If AKLM is congruent to APQR and APQR is congruent to ASTU, then AKLM is congruent to ASTU.
Based on the explanation, statement D is the example of the transitive property of congruence. Therefore, the correct choice is option D.
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