Final answer:
The correct answer choice to support the equation XM + MY = XY, given the definition of congruence, is a. Substitution Postulate of Equality, considering the options provided. The exact justification should cite the Segment Addition Postulate but is not listed.
Step-by-step explanation:
The Substitution Postulate of Equality states that if two things are equal to the same thing, then they are equal to each other. However, the question involves the concept that adding segments end-to-end equals the total length of segments (Segment Addition Postulate). Although the Segment Addition Postulate is what truly justifies the equation, considering the provided options, the closest available choice is a. Substitution Postulate of Equality. The principle behind the equation is the same as adding ordinary numbers such as 2 + 3 = 5 being the same as 3 + 2 = 5 due to the commutative property of addition. However, in geometry, when we refer to the lengths of line segments, there is another specific postulate that states if point M lies between points X and Y, then XM + MY = XY. This would be the most accurate reason if it were provided as an option.