The transitive property of congruence is a fundamental principle that relates to congruent figures. It states that if one shape (like an angle or segment) is congruent to a second shape, and the second shape is congruent to a third shape, then the first shape is congruent to the third shape. It can be expressed generally as: if A ≅ B and B ≅ C, then A ≅ C.
Let's analyze the provided options to see which one exemplifies the transitive property of congruence:
A. This option seems incomplete or contains some typographical errors. It does not express a complete idea or statement that we can associate with the transitive property.
B. This option states that a shape is congruent to itself, which is always true due to the reflexive property of congruence, not the transitive property.
C. This option is similar to option A and seems to contain errors or be incomplete. Apart from that, it appears to suggest that if AKLM is congruent to APQR, then APQR is congruent to AKLM, which is a restatement of the given information using the symmetric property of congruence, not the transitive property.
D. This option states that if AKLM is congruent to APQR and APQR is congruent to ASTU, then AKLM is congruent to ASTU. This is a perfect illustration of the transitive property of congruence, which tells us that if one shape (AKLM) is congruent to a second shape (APQR), and that second shape (APQR) is congruent to a third shape (ASTU), then the first shape (AKLM) must be congruent to the third shape (ASTU).
So, the correct statement that exemplifies the transitive property of congruence is:
D. If AKLM ≅ APQR and APQR ≅ ASTU, then AKLM ≅ ASTU.
