Question

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

Explanation:

Step1: Recall Segment Addition Postulate

The segment addition postulate states that if point \( C \) is between points \( A \) and \( B \), then \( AC + CB = AB \). In other words, for collinear points, the sum of the lengths of two adjacent segments equals the length of the combined segment.

Step2: Identify Coordinates of Points

From the number line:

• \( A \) is at \( -6 \)
• \( B \) is at \( -1 \)
• \( C \) is at \( 2 \)
• \( D \) is at \( 8 \)

Step3: Calculate Lengths of Segments

• \( AB = | -1 - (-6)| = |5| = 5 \)
• \( BC = |2 - (-1)| = |3| = 3 \)
• \( CD = |8 - 2| = |6| = 6 \)
• \( AD = |8 - (-6)| = |14| = 14 \)
• \( BD = |8 - (-1)| = |9| = 9 \)

Step4: Test Each Option

• Option 1: \( AB + BC = 5 + 3 = 8 \), \( AD = 14 \). \( 8

eq 14 \), so false.

• Option 2: \( AB + BC = 8 \), \( CD = 6 \). \( 8

eq 6 \), so false.

• Option 3: \( BC + CD = 3 + 6 = 9 \), \( AD = 14 \). \( 9

eq 14 \), so false.

• Option 4: \( BC + CD = 3 + 6 = 9 \), \( BD = 9 \). \( 9 = 9 \), so true.

Answer:

D. \( BC + CD = BD \)