Which statement reflects the Segment Addition Postulate?

Which statement reflects the Segment Addition Postulate?

• A. The whole segment is equal to the sum of its parts: AB + BC = AC.
• B. The whole segment is equal to the difference of its parts.
• C. The product AB × BC equals AC.
• D. AB is equal to AC plus BC.

Answer: (A)

The Segment Addition Postulate says that if a point B lies on segment AC with B between A and C, then the whole length AC is the sum of the two parts AB and BC. In other words, AB + BC = AC, where AB and BC are the lengths of the pieces you get when you split AC at B. This is why the statement that the whole segment equals the sum of its parts is the correct reflection of the postulate. The other options involve differences, products, or a sum that doesn’t match the whole, which don’t describe how the lengths of a segment relate when you insert a point between its endpoints.

The Segment Addition Postulate says that if a point B lies on segment AC with B between A and C, then the whole length AC is the sum of the two parts AB and BC. In other words, AB + BC = AC, where AB and BC are the lengths of the pieces you get when you split AC at B. This is why the statement that the whole segment equals the sum of its parts is the correct reflection of the postulate. The other options involve differences, products, or a sum that doesn’t match the whole, which don’t describe how the lengths of a segment relate when you insert a point between its endpoints.