Using the segment addition postulate, which is true? A B C D -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 ? AB + BC = AD ? AB + BC = CD ? BC + CD = AD ? BC + CD = BD
The Correct Answer and Explanation is:
The correct equation is BC + CD = BD.
The segment addition postulate states that if a point lies between two other points on a line, the sum of the lengths of the smaller segments equals the length of the larger segment. Using the number line provided in the image, the positions of points A, B, C, and D must be examined. The distances between these points are calculated as follows:
- AB: |-6 – (-2)| = 4
- BC: |-2 – 3| = 5
- CD: |3 – 8| = 5
- AD: |-6 – 8| = 14
- BD: |-2 – 8| = 10
The objective is to determine which equation correctly follows the segment addition postulate. Testing each:
- AB + BC = AD → 4 + 5 = 14 (False)
- AB + BC = CD → 4 + 5 = 5 (False)
- BC + CD = AD → 5 + 5 = 14 (False)
- BC + CD = BD → 5 + 5 = 10 (True)
This confirms that BC + CD = BD is the correct answer.
Understanding this principle allows for solving various problems involving points, distances, and relationships within geometric structures. This equation demonstrates that the total length of segment BD can be calculated by summing the lengths of segments BC and CD, reinforcing the fundamental concept of segment addition. This method is applied in geometry when analyzing distances, constructing proofs, and solving measurement-related problems. Mastery of such principles aids in navigating both theoretical and real-world applications of geometric concepts, particularly in fields requiring precision in spatial reasoning and structure formation.
