Question

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

a) If AEFG = AHJK, then AHJK = AEFG.
b) AEFG = EFG.
c) If AEFG = AHJK, and AHJK = AMNP, then AEFG = AMNP.
d) If EFG = HJK, then AHJK = AMNP.

Answer 1

The example of the transitive property of congruence is statement (c), which accurately demonstrates the logic that if two things are both equal to a third thing, then they are equal to each other.The correct option is c.

Step-by-step explanation:

The question you asked is about identifying which statement is an example of the transitive property of congruence. The correct statement that represents this property is (c) If AEFG = AHJK, and AHJK = AMNP, then AEFG = AMNP. The transitive property states that if one quantity is equal to a second quantity, and the second quantity is equal to a third quantity, then the first quantity is equal to the third quantity. In this context, congruence can be understood as another form of equality, often used in geometry to describe figures that are the same size and shape.

Statement (a) is simply the symmetric property of equality, stating that if one quantity equals another, then those two quantities can be expressed in reverse order. Statement (b) appears to be a typo or incorrectly noted, as AEFG cannot equal part of itself, EFG. Statement (d) does not represent the transitive property because it introduces a second condition (EFG = HJK) without relating it directly back to AHJK = AMNP, thus it doesn't logically follow the rules of the transitive property.The correct option is c.