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 three points \( X \), \( Y \), \( Z \) are collinear and \( Y \) is between \( X \) and \( Z \), then \( XY + YZ = XZ \).

Step2: Analyze the positions of points

From the number line:

• Point \( A \) is at \( -6 \), \( B \) at \( -1 \), \( C \) at \( 2 \), \( D \) at \( 8 \).
• Check each option:
• Option 1: \( AB + BC \). \( AB = |-1 - (-6)| = 5 \), \( BC = |2 - (-1)| = 3 \), \( AB + BC = 5 + 3 = 8 \). \( AD = |8 - (-6)| = 14 \). \( 8

eq 14 \), so false.

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

eq 6 \), false.

• Option 3: \( BC + CD \). \( BC = 3 \), \( CD = |8 - 2| = 6 \), \( BC + CD = 9 \). \( AD = 14 \). \( 9

eq 14 \), false.

• Option 4: \( BC + CD \). \( BC = 3 \), \( CD = 6 \), \( BC + CD = 9 \). \( BD = |8 - (-1)| = 9 \). So \( BC + CD = BD \), true.

Answer:

D. \( BC + CD = BD \)